- 


r 


REESE  LIBRARY 

<)!••  THIC 

UNIVERSITY  OF  CALIFORNIA. 


L 


Accessions  No. 


Class  M>. 


CHAPTERS 


ON 


ELECTEICITT 


AN  INTRODUCTORY    TEXT-BOOK  FOR 
STUDENTS   IN    COLLEGE 


BY 

SAMUEL    SHELDON,    PH.D.  (WURZBURG) 

3TU1FS3SOR  OF  PHYSICS  AND  ELECTRICAL  ENGINEERING,  POLYTECHNIC  INSTITUTE  OP  BROOK1YS 


•        SECOND  EDITION 
WITH  A  COURSE  IN  ELECTRICAL  MEASUREMENTS. 


NEW  YORK 
CHAELES   COLLINS,   PUBLISHER 

AND 

THE  BAKER  &  TAYLOR  CO.,  5  EAST  SIXTEENTH  STREET 


SHELDON'S   CHAPTERS  ON  ELECTRICITY 

COPYRIGHT,  1891 
Br  CHARLES   COLLINS 


SECOND  EDITION 

COPYRIGHT,  1895 
BY  CHARLES  COLLINS 


PREFAO'E 


fTlHESE  Chapters  on  Electricity,  prepared  for  and  included  in 
-*-  the  Fourth  Revised  Edition  of  Olmsted's  College  Philos- 
ophy, are  here  offered  in  a  separate  volume.  They  are  intended 
for  use  as  a  text-book  by  students  in  those  colleges  which  devote 
but  thirty  or  forty  hours  to  the  subject.  The  principles  presented 
are  those  which  ought  to  be  known  by  every  liberally  educated 
person.  The  economy  of  space  necessitated  by  a  clear  and 
thorough  presentation  within  such  limits,  has  required  the  omis- 
sion of  detailed  descriptions  of  appa7*atus  and  of  demonstrative 
experiments.  To  master  these  chapters  will  require  more  effort 
on  the  part  of  a  student  than  to  master  an  equal  number  of  pages 
in  a  more  extended  treatise.  For  the  same  efforts,  however,  he 
will  obtain  a  knowledge  of  a  greater  number  of  principles.  Fur- 
thermore, he  will  more  readily  perceive  the  correlation  between 
different  parts  of  the  subject.  Even  an  ordinary  comprehension 
of  the  subject  signifies  a  knowledge  of  many  of  these  mutual 
relations. 

It  has  been  the  desire  of  the  author  to  present  each  part  of  the 
subject  in  its  most  modern  dress.  This  desire,  however,  has  been 
tempered  by  a  consideration  of  the  intended  functions  of  the  book. 

POLYTECHNIC  INSTITUTE  OF  BROOKLYN, 
June,  1891. 


IN  the  present  edition  a  few  typographical  errors  have  been 
corrected,  and  a  Course  in  Electrical  Measurements  has  been 
added.  This  course  is  written  in  the  form  of  a  laboratory  manual 
in  which  specific  directions  are  given  to  the  student.  The  experi- 
ence of  the  author  has  shown  that  such  a  manual  results  in  a  saving 
of  time  both  to  the  instructor  and  the  student.  The  enthusiasm 
of  the  student  is  better  maintained  when  his  results  are  fairly  ac- 
curate and  of  frequent  occurrence.  A  meagre  laboratory  equipment 
is  sufficient  for  carrying  on  the  course,  and  the  accuracy  of  the  re- 
sults obtained  will  depend  almost  entirely  upon  the  student  and  the 
instructor. 

POLYTECHNIC  INSTITUTE  OF  BROOKLYN, 
July,  1895. 


CONTENTS. 


(The  figure*  rv/vr  to  the  page*,) 

PART   VII.-ELECTBIC1TY   AND   MAGNETISM. 
CHAPTER    I. 

ELECTROSTATICS. —POTENTIAL.— CAPACITY. 

Definition — Common  Indications  of  Electricity — Repulsion,  351  ;  Theories 
of  Electricity — Electric  Series,  352  ;  Conductors  and  Insulators — Cou- 
lomb's Law,  353 ;  Potential,  354 ;  Equipotential  Surfaces,  355 ;  Dif- 
ference of  Potential — Unit  of  Potential,  356  ;  Zero  Potential — Potential 
on  a  Sphere — Capacity,  357  ;  Equipotential  of  Connected  Conductors — 
Position  of  Static  Charge — Distribution  of  a  Charge  on  the  Surface, 
359  ;  Surface  Density— Quadrant 'Electrometer,  360  ;  Problems,  361. 

CHAPTER    II. 

ELECTROSTATIC     INDUCTION. 

Gold-leaf  Electroscope — Phenomena,  362 ;  Induction  Precedes  Attraction, 
363  ;  Quantity  of  the  Induced  Electricity — Condensers,  364 ;  Specific 
Inductive  Capacity,  365  ;  Leyden  Jar— Seat  of  the  Charge,  367  ;  Resid- 
ual Charge — Modern  Theory  of  Condensers,  368  ;  Hertz's  Experiments, 
369  ;  Electrical  Machines— Electrophorus— Holtz  Machine,  370  ;  Effects 
of  Statical  Discharge — Lightning,  372. 

CHAPTER    III. 

MAGNETISM. 

Natural  Magnets — Artificial  Magnets — Poles  of  a  Magnet — Magnetic  Needle, 
373  ;  Attractions  and  Repulsions — North  and  South  Poles'lnseparable — 
Magnetic  Induction,  374 ;  Retentivity  or  Coercive  Force,  375  ;  Law  of 
Magnetic  Force — Unit  Magnet  Pole,  376  ;  Lifting  Power — Laminated 
Magnets,  377 ;  Magnetic  Field— Lines  of  Force,  378  ;  Theory  of  the 
Curvature  of  the  Lines,  379 ;  Fields  from  Several  Magnets,  380 ; 
Strength  or  Intensity  of  Magnetic  Field — Determination  of  the  Strength 
of  a  Field,  381  ;  Hysteresis — Number  of  Lines  of  Force  from  a  Given 
Pole,  382  ;  Magnetic  Susceptibility,  383  ;  Magnetic  Permeability— Mag- 
netic Circuit,  384  ;  Paramagnetism  and  Diamagnetism,  385. 

CHAPTER    IV.  V 

TERRESTRIAL     MAGNETISM. 

The  Earth  a  Magnet — Declination  of  the  Needle — Ispgonic  Curves,  386  ; 
Secular  and  Annual  Variation  —  Diurnal  Variation  —  Magnetometer, 
388  ;  Dip  of  the  Needle,  389  ;  Isoclinic  Curves,  390  ;  Intensity  of  the 
Earth's  Magnetism,  391  ;  Isodynamic  Curves,  392 ;  Variation  in  the 
Strength  of  the  Earth's  Field — Astatic  Needles,  393  ;  Magnetic  Charts 
—The  Declination  Compass — The  Mariner's  Compass,  394  ;  Aurora 
Borealis— Why  the  Earth  is  a  Magnet,  395. 

CHAPTER  V. 
CURRENT    ELECTRICITY. 

Electricity  in  motion — Galvanic  Cells,  396 ;  Electromotive  Force,  397 ; 
Polarization— Types  of  Batteries,  398;  Daniell's  Cell— Leclanche 
Cell,  399 ;  Combustion  of  Zinc — Amalgamation  of  Zincs,  400  ;  Prac- 


V1  CONTENTS. 

tical  Units  of  Current  and  Quantity— Resistance,  401 ;  Influence  of 
Temperature,  402;  Ohm's  Law— Divided  Circuits— Shunts,  403; 
Ratio  of  Currents  in  shunts— Fall  of  Potential,  404;  Resistance 
Boxes  or  Rheostats— Wheatstone's  Bridge,  405  ;  Cells  in  Series  and 
in  Multiple  Arc,  407 ;  Problems,  408. 

CHAPTER    VI. 

ELECTRO -MAGNETISM. 

The  Current's  Lines  of  Magnetic  Force,  409  ;  Effect  of  a  Current  on  a  Mag- 
net,  410  ;  Solenoids,  411  ;  Ampere's  Theory  of  Magnetism,  412  ;  Electro- 
magnets— Magneto- motive  Force,  413 ;  The  Morse  Telegraph  System, 
415;  The  Relay,  417;  Duplex  Telegraphy,  418;  Atlantic  Telegraph 
Cable— Electric  Bells,  420  ;  Galvanometers,  421. 

CHAPTER    VII. 

ELECTRO-DYNAMICS. 

Movements  of  Conductors  Carrying  Currents — Parallel  Currents,  423  ;  Cur- 
rents not  Parallel,  424  ;  Continuous  Rotation  Produced  by  Mutual  Ac- 
tion of  Currents,  425  ;  Electro-dynamometer,  426. 

CHAPTER    VIII. 
ELECTRO-MAGNETIC   INDUCTION. 

Currents  of  Electricity  Produced  by  Induction— Methods  of  Producing  the 
Inducing  Field,  427  ;  Lenz's  Law— Self-induction,  429  ;  Coefficients  of 
Mutual  and  Self-induction — Induced  Currents  from  the  Earth,  430 ; 
Arago's  Rotations— Induction  Coils,  431 ;  The  Telephone,  432 ;  The 
Blake  Transmitter,  433  ;  Dynamos,  434  ;  Electric  Motors,  436. 

CHAPTER    IX. 

ELECTRO-CHEMISTRY   AND    ELECTRO-OPTICS. 

Electrolytes,  436;  Electrolysis  of  Sulphuric  Acid— Metallic  Salts,  437; 
Faraday's  Laws — Voltameters,  438  ;  Theory  of  Electrolysis — Electro- 
plating, 439  ;  Electrotyping  —  Counter  -  Electromotive  Force,  440  ; 
Storage  Batteries,  441 ;  Capillary  Electrometer,  442 ;  Light  and  Elec- 
tricity— Double  Refraction  from  Electrostatic  Strain,  443 ;  Magneto- 
optic  Twisting  of  the  Plane  of  Polarized  Light— Rotation  of  the  Plane 
by  Reflection — Photo-Electric  Properties  of  Selenium,  444. 

CHAPTER    X. 

THE   RELATIONS   BETWEEN   ELECTRICITY    AND    HEAT. 

Power  of  the  Electrical  Current,  445  ;  Heat  Developed  in  a  Conductor — 
Rise  in  Temperature  of  the  Conductor,  446  ;  Hot  Wire  Ammeters  and 
Voltmeters,  447  ;  Electric  Welding — The  Electric  Arc,  448  ;  Incan- 
descent Electric  Lamps  —  Thermo-Electricity,  449  ;  Thermo-Electric 
Pile— Peltier  Effect,  450  ;  The  Electrical  Units,  451. 

A  COURSE  IN  ELECTRICAL  MEASUREMENTS. 

Intro  duct  017,  453 ;  Resistances,  455 ;  Battery  Resistances,  460 ;  Com- 
parison of  Electromotive  Forces,  464 ;  Measurement  of  Currents, 
466  ;  Condensers,  468  ;  Magnetism,  469 ;  Calibrations,  472. 


f  OF  THE  ^\ 

(UNIVERSITY) 

x.  w  s 


PART    VII. 

ELECTEIOITT    AND    MAGNETISM, 


CHAPTER   I. 

ELECTROSTATICS.— POTENTIAL.— CAPACITY. 

557.  Definition. — The  name  Electricity,  from  the  Greek  word 
for  amber,  is  given  to  a  peculiar  agency,  which  causes  mutual 
attractions  or  repulsions  between  light  bodies,  and  which,  under 
proper  conditions,  also  produces  heat,  light,  sound,  and  chemical 
decomposition. 

Lightning  and  thunder  are  familiar  illustrations  of  the  intense 
action  of  this  agency.  , 

558.  Common  Indications  of  Electricity. — If  amber,  seal- 
ing-wax, or  any  other  resinous  substance,   be  rubbed  with  dry 
^woollen  cloth,  fur,  or  silk,  and  then  brought  near  the  face,  the 
excited  electricity  disturbs  the  downy  hairs  upon  the  skin,  and 
thus  causes  a  sensation  like  that  produced  by  a  cobweb.     When 
Tulcanite  is  strongly  excited,  it  gives  off  a  spark  to  the  finger  held 
toward  it,  accompanied  by  a  sharp  snapping  noise.     A  sheet  of 
writing-paper,  first  dried  by  the  fire,  and  then  laid  on  a  table 
•and  rubbed  with  India-rubber,  becomes  so  much  excited  as  to 
adhere  to  the  wall  of  the  room  or  any  other  surface  to  which  it  is 
applied.     As  the  paper  is  pulled  up  slowly  from  the  table  by  one 
•edge,  a  number  of  small  sparks  may  be  seen  and  heard  on  the 
under  side  of  the  paper.     In  dry  weather,  the  brushing  of  a  gar- 
ment causes  the  floating  dust  to  fly  back  and  cling  to  it. 

Bodies  are  said  to  be  electrically  excited  when  they  show  signs 
of  electricity  in  consequence  of  some  mechanical  action  performed 
upon  them,  as  in  the  experiments  already  described. 

A  body  is  electrified  when  it  receives  electricity,  by  communica- 
tion, from  another  body  already  excited  or  electrified. 

559.  Repulsion.  —  An   electrically   excited    body   does   not 
always  produce  attraction.     It  will  be  noticed  that  pith-balls,  after 


352  ELECTRICITY     AND     MAGNETISM. 

coining  in  contact  with  an  electrified  body,  which  has  attracted 
them,  are  repelled.  They  have  received  a  portion  of  the  elec- 
tricity which  attracted  them  and  repulsion  is  the  result.  This 
repulsion  can  be  made  much  more  apparent  if  an  electrified  vul- 
canite rod  be  suspended  in  a  wire  loop  at  the  end  of  a  silk  thread 
and  then  a  similarly  electrified  rod  be  approached  to  it.  The 
suspended  rod  can  be  made  to  revolve  rapidly  because  of  the 
repulsion. 

560.  Theories  of  Electricity. — As  to  the  exact  nature  of 
electricity  science  is  still  in  the  dark,  though  probably  the  dark- 
ness which  precedes  dawn. 

Symmer  proposed  a  "two-fluid"  theory.  He  supposed  every 
unelectrified  body  to  contain  equal  quantities  of  two  opposite 
kinds  of  impooderable  electric  fluid.  In  equal  quantities  they 
neutralized  each  other.  But  if,  by  friction  or  other  means,  the 
amount  of  one  fluid  be  made  to  exceed  that  of  the  other,  then 
the  body  becomes  positively  or  negatively  electrified.  According 
to  this  theory  two  positively  or  two  negatively  electrified  bodies 
repel  each  other ;  a  positively  electrified  body  and  a  negatively 
electrified  body  attract  each  other. 

Franklin  modified  this  into  a  "  one-fluid  "  theory.  Every  body 
contains  its  own  normal  amount  of  one  electric  fluid.  This  amount 
is  increased  or  decreased  when  rubbed  by  another  body.  The 
surplus  amount  is  obtained  from  or  given  up  to  this  second  body.. 
The  body  with  more  than  its  normal  amount  is  positively  elec- 
trified, and  negatively  electrified  when  it  has  less  than  this  amount. 

Lodge  maintains  that  electricity  is  the  luminiferous  ether  itself. 
He  arrives  at  this  conclusion  after  considering  a  great  number  of 
electrical  phenomena  which  demand  the  ether  for  their  proper 
explanation. 

Without  adopting  any  theory,  electrical  laws  and  phenomena 
may  be  understood  by  considering  the  fact  that  a  body  may  be 
subject  to  two  opposite  electrical  conditions.  It  may  be  positively 
or  negatively  electrified.  The  law  regarding  attraction  and  repul- 
sion then  is : 

Similarly  electrified  bodies  repel  each  other,  and  dissimilarly  elec- 
trified bodies  attract  each  other. 

561.  Electric   Series. — If  two  bodies  are  rubbed  together, 
one  of  them  is  electrified  positively  and  the  other  negatively.     One 
of  these  bodies,  if  rubbed  by  a  third,  may  be  oppositely  electrified 
to  what  it  was  in  the  first  case.     Silk,  when  rubbed  with  glass,  is- 
negatively  electrified;  but  rubbed  with  sulphur,  it  receives  a  pos- 
itive  charge.      In   the    following    series   each   member   becomes 


UNIVERSIT 


COULOMB'S    LA 


353 


positively  charged  when  rubbed  on  one  following  it,  negatively 
when  rubbed  on  one  preceding  it :  fur,  wool,  resin,  glass,  cotton, 
silk,  wood,  metals,  sulphur,  india-rubber,  gutta-percha. 

562.  Conductors  and  Insulators. — When  a  glass  or  vul- 
canite tube  is  rubbed  with  cat's  fur,  it  shows  that  it  has  become 
electrified  by  attracting  light  articles.  If  a  metal  rod  be  substi- 
tuted for  the  glass  one,  no  attraction  will  be  evidenced.  This  is 
not  because  the  metal  was  not  electrified  by  the  rubbing,  but 
because  the  electricity,  as  soon  as  generated,  escaped,  through  the 
rod  itself  and  the  hand  holding  it,  to  the  ground.  If  the  rod  be 
held  by  a  glass  or  hard-rubber  handle  and  then  rubbed,  it  will 
attract  as  the  glass  did.  This  shows  that  some  substances,  as 
metals,  allow  electricity  to  pass  freely  through  them,  while  others, 
as  glass,  almost  entirely  prevent  its  passage.  The  first  class  of 
substances  are  called  conductors,  the  latter  class  non-conductors  or 
insulators.  Some  substances  neither  conduct  nor  insulate  well,  but 
lie  between  the  two  classes.  The  following  is  a  table  of  substances 
arranged  in  the  order  of  their  electrical  conductivity : 


CONDUCTORS. 
1.  Metals. 
2.  Charcoal. 
3.  Graphite. 

4.  Acids. 
5.  Sea-water. 
6.  Vegetables. 
7.  Animals. 

8.  Wood. 
9.  Silk. 
10.  India-rubber. 
11.  Porcelain. 

12.  Glass. 
13.  Shellac. 
14.  Vulcanite. 
INSULATORS. 

A  conductor  mounted  upon  or  suspended  by  an  insulator  is  said 
to  be  insulated. 

A  method  for  determining  the  conductivity  of  substances  is  to 
suspend  two  pith-balls  by  moistened  threads  from  a  metal  insulated 
hook.  Upon  communicating  a  charge  of  electricity  to  the  balls 
they  will  stand  out  away  from  each  other,  owing  to  the  repulsion 
between  the  same  kinds  of  electricity  on  each.  If,  now,  one  end  of 
the  substance,  whose  conductivity  is  to  be  determined,  be  held  in 
the  hand  and  the  other  be  touched  to  the  hook  from  which  the 
faalls  are  suspended,  the  rapidity  with  which  the  balls  fall  toward 
each  other  determines  the  conductivity.  If  they  fall  instantly,  the 
substance  is  a  good  conductor.  If  they  remain  separated,  the  sub- 
stance is  a  good  insulator.  After  an  insulator  or  an  insulated  con- 
ductor has  been  charged  with  electricity,  the  electricity  of  necessity 
remains  at  rest,  and  is,  for  this  reason,  called  statical  electricity.  If, 
now,  it  be  connected,  by  means  of  a  conducting  wire,  with  the 
moist  earth,  it  will  pass  off  instantly  to  the  earth.  During  the 
time  of  its  passage  it  is  called  dynamical  electricity.  If  by  chemical 
or  other  means  the  flow  be  maintained,  then  the  dynamical  elec- 
tricity is  called  galvanic  or  voltaic. 

563.  Coulomb's  Law. — Coulomb  showed  that,  correspond- 


354:  ELECTRICITY    AND     MAGNETISM. 

ing  to  Newton's  law  of  gravitation,  the  force  of  attraction  between 
dissimilarly  electrified  bodies  and  the  force  of  repulsion  between  sim- 
ilarly electrified  bodies  is  directly  proportional  to  the  product  of  the 
quantities  of  electricity  and  inversely  proportional  to  the  square  of  the 
distance  between  the  bodies. 

If  we  represent  the  force  by  /  dynes,  the  distance  by  r  centi- 
metres, and  the  quantities  of  electricity  by  q  and  q'}  then  we  can 
indicate  the  law  by  the  equation 


If  these  magnitudes  be  connected  by  the  sign  of  equality,  a  proper 
unit  of  quantity  must  be  had.  Letting  /  =  1  dyne,  r  =  1  centi- 
meter, and  q  =  q',  then  g2  =  1  and  q  =  ±  1.  Hence  we  may  define- 
the  unit  of  electrical  quantity  as  follows  : 

One  unit  of  electricity  is  that  quantity  which,  when  placed  at  a  dis- 
tance of  one  centimetre  from  a  similar  and  equal  quantity,  repels  it 
with  a  force  of  one  dyne. 

If  the  quantity  of  electricity  be  spread  over  a  body  of  some 
size,  as  a  sphere,  then  the  distance  r  must  be  measured  from  some 
point  as  the  centre  of  the  sphere.  This  is  evidently  for  the  same 
reason  as  in  gravitation,  where  the  distance  is  measured  from  the- 
centre  of  gravity. 

It  must  be  borne  in  mind  that  the  unit  of  quantity  here  given- 
is  based  upon  the  force  exerted  by  two  statical  quantities  of  elec- 
tricity. Another  unit,  based  upon  the  electro-magnetic  force,  will 
be  mentioned  later. 

564.  Potential.  —  Whenever  a  body  is  lifted  vertically  away 
from  the  earth,  the  work  performed  in  lifting  it  has  been  trans- 
formed into  potential  energy.  The  body  has,  because  of  the 
attraction  between  it  and  the  earth,  a  potential  energy  capable  of 
doing  exactly  the  same  number  of  ergs  or  foot-pounds  of  work  as 
were  used  in  raising  it  to  its  position  (Art.  36).  Similarly,  if  two 
conductors,  charged  with  the  same  kind  of  electricity,  be  ap- 
proached towards  each  other,  a  certain  number  of  ergs  of  work 
will  have  been  performed,  owing  to  the  repulsion  between  them. 
(A  more  perfect  analogy  would  be  to  suppose  two  dissimilarly 
charged  conductors  to  be  separated.)  The  work  which  has  been 
performed  is  also  changed  into  potential  energy  between  the  con- 
ductors. The  amount  of  energy  made  potential  depends  upon  the 
quantities  of  electricity  on  each  of  the  conductors,  and  upon  the 
distance  through  which  they  have  been  moved  toward  each  other. 
For  energy  is  measured  by  the  work  it  can  do,  and  work  in  ergs- 
equals  the  product  of  the  force  in  dynes  by  the  distance  in  centi- 


EQUIPOTENTIAL    SURFACES.  355 

metres  through  which  it  has  acted.  Now  the  force  of  repulsion 
between  the  two  conductors  equals  the  product  of  their  quantities 
divided  by  the  square  of  their  distance  apart. 

Suppose  one  of  the  conductors  to  have  any  charge  and  to 
be  fixed  immovably.  Then  let  three  charges  of  respectively  1,  2, 
and  3  units  of  quantity  be  successively  approached,  between  the 
same  limits,  towards  the  first  conductor.  In  the  first  case  a  cer- 
tain amount  of  energy  will  have  been  made  potential ;  in  the 
second  case  twice  as  much,  and  in  the  third  three  times  as  much. 
Evidently  a  certain  amount  of  the  energy  made  potential  is  owing 
to  the  immovable  charge,  and  this  amount  is  the  same  in  each 
case.  The  condition  of  the  space  around  an  electrified  body  is 
termed  the  potential,  owing  to  that  charge.  To  obtain  a  quanti- 
tative expression  for  it, 'the  movable  charge  must  be  taken  of  unit 
quantity.  It  must  also  be  considered  that  the  work  necessary  to 
approach  an  unit  through  a  given  distance  is  not  as  great  as  to 
approach  it  through  twice  that  distance.  Considering  these  two 
points,  we  have  the  definition  of  electrostatic  potential : 

The  potential  at  any  point  is  the  work  that  must  be  spent  upon  a 
unit  of  positive  electricity  in  bringing  it  up  to  that  point  from  an 
infinite  distance. 

If  the  immovable  charge  be  negative,  no  work  would  be 
required  to  move  up  a  positive  unit ;  on  the  contrary,  work  would 
be  performed  by  the  unit  in  travelling.  Hence  the  potential, 
owing  to  a  negative  charge,  is  negative  potential.  It  is  convenient 
to  consider  it  so. 


565.  Equipotential  Surfaces. — If  the  charge  of  electricity 
be  supposed  to  lie  on  a  small  sphere,  then  some  point  can  be 
found  on  every  possible  radius  of  the  sphere  produced  where  the 
potential  will  be  the  same.  That  is,  it  would  require  the  same 
amount  of  work  to  bring  a  positive  unit  of  electricity  from  an 
infinite  distance  out  on  each  radius  to  this  point.  In  the  case  of  a 
sphere  being  charged,  these  points  would  be  equally  distanced 
from  the  centre  of  the  sphere.  If  now  these  points  be  connected 
together,  a  spherical  surface  will  result.  Any  such  surface  which 
contains  only  points  of  the  same  potential  is  called  an  equipotential 
surface. 

In  order  that  an  equipotential  surface  may  be  spherical,  the 
charge  must  lie  upon  a  sphere  and  must  be  free  from  other  electri- 
fied bodies.  If  the  electrified  body  be  irregular  in  shape,  the 
equipotential  surfaces  will  be  correspondingly  so. 

To  transfer  a  quantity  of  electricity  from  one  point  in  an  equi- 
potential surface  to  another  in  the  same  surface  requires  no  work  to 


356  ELECTRICITY    AND     MAGNETISM. 

be  performed.  For  while  it  may  require  work  to  move  the  charge 
in  one  direction  from  the  surface,  it  will  require  a  negative  expen- 
diture of  work  to  bring  it  back  again,  i.e.,  the  attraction  or  repul- 
sion between  the  electricities  performs  the  work. 

566.  Difference  of  Potential. — In  the  consideration  of  most 
problems  in  electricity  involving  the  idea  of  potential,  the  potential 
of  two  points  is  required.     However,  it  is  not  the  absolute  poten- 
tial of  each  of  the  points,  but  the  difference  of  potential  between 
them  which  is  considered.     If  it  requires  a  certain  number  of  ergs 
to  bring  a  unit  of  positive  electricity  from  an  infinite  distance  up 
to  a  given  point,  and  more  ergs  to  bring  it  up  to  a  second  point, 
then  this  extra  work  is  what  would  be  required  to  move  the  unit 
from  the  first  to  the  second  point.     This  number  of  ergs  is  then 
the  measure  of  the  difference  of  potential  between  the  two  poiiits. 
Hence  we  obtain  the  definition  : 

The  unit  difference  of  potential  is  that  which  must  exist  between 
two  points,  that  one  erg  may  be  required  to  move  a  positive  unit 
of  electricity  from  one  to  the  other. 

567.  Unit  of  Potential. — The  difference  of  potential  between 
two  points,  a  and  6,  Fig.  315,  at  distances  r  and  r'  from  a  quantity 

FIG.  315. 


of  electricity  q,  is  measured  by  the  work  necessary  to  move  a 
positive  unit  of  electricity  from  6  to  a. 

This 

work  —  (average)  force  x  distance  through  which  it  is  overcome. 
The  distance  =  r'  —  r. 


Force  at  a  .=  -^-  (  ,      ,  * 

}•  average  force  =  *  '  - 
Force  at  b  —  -75- 


r 
Hence  the  difference  of  potential 

Va  ~~    Vh  =  rT  (T  '  q  \~r  ~ 

This  equation  for  the  difference  of  potential  between  two  points 
enables  us  to  obtain  an  equation  for  the  absolute  potential  Va  at 

*  That  this  is  a  true  average  can  be  proved  by  a  simple  application  of  the 
calculus. 


CAPACITY.  357 

any  point  a.  We  have  only  to  suppose  that  the  second  point  b  is 
removed  to  an  infinite  distance,  where  its  potential  F5  =  0,  and 
r'  =  oo  .  Hence 


Or,  in  general, 

The  potential,  F,  of  any  point  at  a  distance,  r,  from  a  quantity  of 
electricity,  q,  is  expressed  by  the  equation, 

F=i. 

r 

From  this  equation,  supposing  q  and  r  each  equal  to  unity,  we  ob- 
tain the  definition : 

The  unit  potential  is  that  due  to  a  unit  quantity  of  electricity  at  a 
distance  of  one  centimetre. 

The  potential  at  a  point  owing  to  several  charges  of  electricity 
is  equal  to  the  sum  of  the  potentials  at  that  point  due  to  each 
charge  taken  separately.  Thus,  if  quantities  of  electricity  q,  q',  and 
q"  a  -e  at  distances  r,  r'.,  and  r"  from  a  point,  the  potential  at  that  point 


568.  Zero  Potential. — At  an  infinite  distance  away  from  any 
electrified  body  the  potential  would  evidently  be  zero.     If  a  pos- 
itive charge  were  brought  near,  the  potential  would  become  positive, 
and  negative  for  a  negative  charge.     In  practice  it  is  convenient  to 
take  the  earth  as  a  standard  zero,  with  which  all  other  potentials 
may  be  compared.     This  assumption  is  analogous  to  the  use  of  the 
sea-level  as  the  zero  in  measuring  the  heights  of  mountains  instead 
of  the  centre  of  the  earth. 

569.  Potential   on   a    Sphere.  —  By   discussing   the   equa- 
tions  in  Art.  567,  and  supposing  r  equal  to  zero,  one  might  be  led 
io  think  that  the  potential  would   be  infinite.     But  it  must  be 
remembered  that,  just  as  in  gravitation,   there  is  a  centre  from 
which  all  electric  force  apparently  works.     In  the  case  of  the  earth 
all  attraction  is  toward  the  centre  of  gravity.     With  an  electrified 
sphere  all  action  comes  from  the  centre  of  the  sphere.     The  elec- 
tricity (Art.  572)  lies  upon  the  surface  of  it,  but  the  resultant  of 
all  attractions  from  all  the  particles  of  electricity  passes  through 
the  centre.     Thus  a  point  in  the  electricity  itself  on  a  charged 
conductor  has  a  finite  potential,  and,  in  the  case  of  a  sphere,  it  is 
equal  to  the  quantity  of  electricity  divided  by  the  radius  of  the  sphere. 

570.  Capacity. — Suppose  that  a  point  on   the  surface  of  a 
charged  spherical  conductor,  i.e.,  any  point  in  the  electiicify  itself, 


358  ELECTRICITY    AND    MAGNETISM. 

to  have  a  certain  potential.  If,  now,  the  radius  of  the  sphere  be 
supposed  to  grow  smaller,  while  the  quantity  of  electricity  remains 
the  same,  then  the  potential  will  evidently  increase  as  the  radius 

decreases,  because  the  potential  V  —  —  •     Thus  a  large  sphere,  e.g., 

the  earth,  can  hold  a  large  quantity  of  electricity  without  having  a 
high  potential.  This  ratio  between  quantity  and  potential  of  elec- 
tricity in  a  conductor  is  termed  the  electrostatic  capacity  of  the 
conductor.  ^Representing  this  by  C,  we  have  the  definition  in  the 
form  of  an  equation  : 

0_0 

°~  V 

From  this,  by  supposing  Q  and  V  each  equal  to  unity,  we  have  the 
definition, 

That  conductor  has  a  unit  of  electrostatic  capacity,  which  requires- 
a  unit  quantity  of  electricity  to  raise  its  potential  from  zero  to  one. 

Applying  the  above  equation  to  a  sphere  of  radius  r  we  have 

v-Q-  Q, 

-  c  --  7' 

whence  we  see  that  the  electrostatic  capacities  of  spheres  are 
equal  to  their  radii.  Accordingly  a  sphere  of  1  centimetre  radius 
has  a  unit  capacity. 

A  conductor,  no  matter  what  its  shape,  will  have  a  capacity, 
and  we  may  say  that, 

The  capacity  of  any  conductor  is  equal  to  the  number  of  units 
of  quantity  of  electricity  necessary  to  raise  its  potential  from  zero  to 
unity. 

571.  Equipotential  of  Connected  Conductors. — When  a 
conductor  is  charged  with  electricity  each  particle  strives  to  get 
out  of  the  reach  of  its  neighbors,  because  of  the  natural  repulsion 
between  like  kinds  of  electricity.  The  particle,  however,  cannot 
escape,  because  the  dry  air  is  an  insulator.  If,  now,  it  be  con- 
nected, by  means  of  a  conducting  wire,  with  the  earth,  the  par- 
ticle, followed  by  others,  will  flow  off  to  the  earth.  Now  the  earth, 
having  such  a  very  large  radius,  would  require  an  enormous 
quantity  of  electricity  to  raise  its  potential  even  an  infinitesimal 
amount.  The  result  is  that  the  potential  of  the  conductor  and 
earth  are  both  reduced  to  zero.  Suppose,  however,  that  instead 
of  being  connected  with  the  earth  it  had  been  connected  to  another 
insulated  conductor.  The  particles  escaping  from  the  first  con- 
ductor would  gradually  raise  the  potential  of  the  second  until  a 
particle,  at  some  place  on  the  connecting  wire,  would  be  equally 
repelled  by  the  charges  on  each  conductor,  and  would  accordingly 


DISTRIBUTION.  359* 

remain  at  rest.  Now  it  will  be  found  that,  just  as  when  two 
vessels,  one  of  which  contains  water,  when  connected  by  a  tube  at 
the  bottom,  will  allow  the  flow  of  water  until  the  level  in  both  is 
the  same,  so  with  these  conductors,  the  potentials  of  both  will  have 
become  the  same  because  of  the  connecting  wire.  Furthermore, 
just  as  is  the  case  with  the  connected  vessels  of  water,  it  makes  no 
difference  whether  the  second  conductor  had  originally  a  charge  of 
electricity  or  not.  The  potential  of  all  electrostatically  charged 
conductors  becomes  the  same  when  connected  together. 

If  the  potential  of  connected  conductors  becomes  the  same, 
then  it  is  quite  evident  the  total  quantity  of  electricity  must  be  so 
divided  that  each  conductor  shall  have  a  quantity  in  direct  propor- 
tion to  its  capacity.  This  must  necessarily  follow  from  the  defi- 
nition of  capacity  at  the  end  of  Art.  570.  Thus  three  connected 
conductors  of  capacities  1,  2,  and  3  would  have  respectively  one-, 
two-,  and  three-sixths  of  the  total  quantity  of  electricity  upon  them. 

572.  Position  of  Static  Charge. — A  statical  charge  of  elec- 
tricity always  resides  on  the  outside  surface  of  a  conductor.     It 
also  resides  on  the  outside  of  the  geometrical  figure  of  the  con- 
ductor.    Thus,  if  a  charge  be  communicated  to  a  wire  bird-cage, 
it  will  reside  wholly  on  the  outside  half  of  the  wires  and  none  will 
lie  on  the  inside.     This  may  be  shown  in  many  ways. 

If  a  hollow,  insulated,  conducting  cylinder  (Fig.  316)  be  pro- 
vided with  two  suspended  pith  balls  in  the  interior  and  two  on  the 
exterior,  and  a  charge  of  electricity  be  communi-  _ 

cated  to  it,  the  outside  balls  will  diverge,  owing 
to  the  repulsion  of  like  electricities.  The  inside 
balls  will,  on  the  other  hand,  remain  at  rest.  It 
makes  no  difference  whether  the  charge  be  com- 
municated to  the  inside  or  outside.  As  soon  as  it 
has  been  communicated  the  inside  balls  drop  to 
their  normal  position. 

In  calculating  the  capacities  of  conductors,  it 
makes  no  difference  whether  a  conductor  is  solid 
or  hollow. 

573.  Distribution   of   a   Charge   on   the 
Surface. — Statical  electricity  resides  at  the  sur- 
face of  a  body,  as  we  have  seen,  but  is  not  uni- 
formly diffused  over  it,  except  in  the  case  of  the  sphere.     In  gen- 
eral, the  more  prominent  the  part,  and  the  more  rapid  its  curvature, 
the  more  intensely  is  the  electricity  accumulated  there. 

In  a  long,  slender  rod  the  density  is  greatest  at  the  ends,  nearly 
the  whole  charge  being  collected  at  these  points.  On  a  sphere, 


% 

•FT-  T-<   _ 


360  ELECTRICITY     AND     MAGNETISM. 

not  influenced  by  other  electrified  bodies,  the  density  is  uniform, 
as  illustrated  in  Fig.  317,  the  dotted  line  denoting  by  its  constant 
distance  from  the  surface  the  uniform  distribution  of  the  charge. 
Fig.   318  represents  the  varying   density  upon   an   ellipsoid. 

FIG.  317.  FIG.  318, 


The  two  ellipsoids  are  similar,  and  the  ellipsoidal  shell  included 
between  them  represents  the  densities  at  various  points.  In  this 
case  the  densities  at  any  two  points  of  the  ellipsoid  are  nearly 
proportional  to  the  diameters  through  those  points. 

The  student  must  remember  that  the  charge  does  not  form  a 
layer  upon  the  body  in  any  sense  whatever,  and  that  the  above 
figures  are  given  merely  to  aid  the  memory  in  retaining  the  law 
of  distribution. 

574.  Surface  Density. — The  greater  the  quantity  of  elec- 
tricity on  a  given  conductor,  the  greater  the  tendency  is  for  the 
electricity  to  escape  to  surrounding  objects.  . 

The  surface  density  at  any  point  of  a  surface,  when  the  dis- 
tribution is  uniform,  is  the  quantity  of  electricity  per  square 
centimetre  of  surface. 

If  Q  units  of  electricity  reside  on  S  square  centimetres  of  sur- 
face, then  the  surface  density  d  is  represented  by  the  formula 

•'-* 

The  surface  of  a  fine  point  is  very  small,  hence,  if  there  is  any 
quantity  of  electricity  supplied  to  it,  the  density  becomes  very 
great  and  the  charge  escapes  into  the  air. 

575.  Quadrant  Electrometer. — This  instrument  is  used  for 
determining  very  accurately  differences  of  electrical  potential.     A 
simple  form,  suited  for  qualitative  work,  is  shown  in  Fig.  319. 
Four  like  pieces  of  metal  are  suspended,  by  conducting  rods,  from 
the  insulating  top  of  a  glass  case.     They  are  symmetrically  placed 
(as  shown  in  the  small  figure)  and   are  fixed  in  position.     Over 
these    quadrants,   as    they   are   termed,   swings   a   flat   aluminum 
needle,  suspended  by  a  wire  of  small  diameter.     This  prolonged 
suspension  hangs  in  a  glass  chimney,  placed  upon  the  top  of  the 


QUADRANT    ELECTROMETER. 


361 


case.     A  small  mirror,  Jf,  is  attached  to  a  rigid  prolongation 
of  the  suspension,  prolonged  beneath  the  needle.     This  mirror 

FIG.  319. 


serves  to  reflect  the  image  of  a  scale.  S,  through  a  reading  tele- 
scope, L,  by  means  of  which  deflections  of  the  needle  can  be 
observed. 

To  use  the  instrument,  the  needle  is  charged,  through  its 
suspending  wire,  to  a  constant  potential.  This  may  be  done  by 
connecting  G  with  the  knob  of  a  charged  Leyden  jar.  The 
diagonally  opposite  quadrants  are  connected  together,  and  the 
two  pairs  connected  with  the  points  whose  difference  of  potential 
is  to  be  determined.  Now  suppose  that  2  and  4  (small  diagram) 
were  of  higher  potential  than  1  and  3.  They  would  exert  a  greater 
force  upon  the  needle  than  1  and  3,  and  according  to  the  sign  of 
the  charge  on  the  needle,  would  cause  rotation  of  the  needle  in  one 
direction  or  another.  The  needle,  which  was  held  in  the  zero 
position  by  the  torsion  of  its  suspension,  would  come  to  rest  at  a 
place  where  the  force  of  torsion  was  equal  and  opposed  to  the 
electrical  force.  For  small  deflections  the  forces  are  proportional 
to  the  tangents  of  the  angle,  i.e.,  to  the  readings  of  the  scale. 

For  very  accurate  work  many  complicated  attachments  are 
added  to  this  simple  form. 

Problems. 

1.  Two  conductors,  of  capacity  10  and  15  respectively,  are  con- 
nected by  a  fine  wire  and  a  charge  of  1000  units  is  divided  between 
them  :  find  the  charge  which  each  takes,  and  the  potential  to 
which  each  is  raised. 


362  ELECTRICITY    AND    MAGNETISM. 

2.  Three  spheres  of  radii  1,  2,  and  3  cm.  are  charged  to  poten- 
tials 3,  2,  and  1  respectively,  and  are  then  connected  by  a  fine 
wire  :  what  is  their  common  potential  ? 

3.  Two  spheres,  of  capacity  2  and  3,  are  charged  respectively  to 
potentials  5  and  10 :  what  will  be  their  common  potential,  if  they 
are  placed  in  electrical  connection  ? 

4.  Two  spheres,  of  2  and  6  cm.  radius,  are  charged  respectively 
with  80  and  30  units  of  electricity ;  compare  their  potentials.     If 
they  are  connected  by  a  fine  wire,  how  much  electricity  will  pass 
along  it  ? 

5.  Twelve  units  of  electricity  raises  the  potential  of  a  conductor 
from  0  to  3 :  what  is  its  capacity  ? 


CHAPTEE   II. 

ELECTROSTATIC    INDUCTION. 

576.  Gold-leaf  Electroscope. — The  gold-leaf  electroscope 
is  a  delicate  instrument  for  detecting  the  presence  of  electric- 
ity.    It  consists  (Fig.  320)  of  a  folded  strip 

FIG.  320.  Of    gold-leaf,    suspended   from   the   end   of 

a  brass  rod,  which  penetrates  the  stopper 
of  a  glass  insulating  receiver.  The  outside 
end  of  the  rod  is  provided  with  a  brass 
ball.  Whenever  a  charge  of  electricity  is 
communicated  to  the  ball  the  gold-leaves 
partake  of  it  and  diverge  from  each  other, 
because  of  the  repulsion  of  like  kinds  of 
electricity.  The  sides  of  the  receiver  are 
provided  with  strips  of  tin-foil,  which  are 
in  electrical  communication  with  the  earth 
through  the  base.  The  object  of  these  is  to 
prevent  the  rupturing  of  the  gold-leaves  by 
the  sudden  communication  of  too  great  a 
charge.  Upon  receiving  such  a  charge  the}'  diverge  aiid  com- 
municate it  to  the  tin-foil  and  it  escapes  thence  to  the  earth. 

577.  Phenomena  of  Induction. — Whenever  an  electrified 
t>ody  is  approached  toward  the  brass  ball  of  an  electroscope,  it 
will  be  noticed  that,  while  it  is  even  a  great  distance  away  from 
it,  the  gold-leaves  begin  to  separate  and  show  the  presence  of 
electricity  upon  them.     This  electricity  is  the  result  of  the  presence 


• 
EXPLANATION    OF    ATTRACTION.  363 

of  an  electrified  body  in  the  neighborhood  and  is  called  induced 
electricity.  The  process  under  which  it  was  generated  is  termed 
electrostatic  induction. 

Whenever  a  charged  conductor  is  brought  near  to  an  uncharged 
conductor,  and  is  separated  from  it  only  by  an  insulator,  which  in 
this  case  is  called  a  dielectric,  the  uncharged  conductor  undergoes 
an  electrical  change.  The  side  which  is  toward  the  first  con- 
ductor is  charged  with  an  opposite  kind  of  electricity,  while  the 
remote  side  has  a  charge  of  same  kind  as  the  original  charge. 

Thus  (Fig.  320),  if  a  negatively  electrified  piece  of  hard  rubber 
be  brought  near  to  the  gold-leaf  electroscope  and  is  separated  from 
it  by  air  for  a  dielectric,  there  will  be  positive  electricity  induced 
on  the  nearer  side  of  the  electroscope,  which  is  the  ball,  and  neg- 
ative on  the  remote,  which  includes  the  gold-leaves.  The  leaves 
accordingly  diverge.  The  electricity  on  A  is  called  the  inducing 
charge,  that  in  the  electroscope  the  induced  charge. 

Whenever  an  insulated  conductor,  which  contains  the  two  kinds 
of  induced  electricity  and  is  still  under  the  influence  of  the  induc- 
ing charge,  is  connected  with  the  earth,  the  electricity  of  the  same 
kind  as  the  inducing  charge  will  escape  to  the  earth.  This  is 
because  of  the  repulsion  between  like  kinds  of  electricity.  It  is 
equally  true  whether  the  near  or  remote  side  of  the  conductor  is 
connected  to  the  earth. 

The  remaining  opposite  kind,  however,  cannot  escape  because 
of  the  attraction  exerted  by  the  original  inducing  charge.  If  now 
the  earth  connection  be  removed,  it  will  be  found  that  only  a  small 
portion  of  the  original  inducing  charge  can  escape  when  connected 
to  the  earth.  It  is  held  in  place  by  an  opposite  kind  of  electricity, 
which  it  has  itself  produced.  These  two  opposite  electricities, 
separated  by  a  dielectric,  are  said  to  be  bound,  while  electricity 
free  to  follow  an  earth  connection  is  called  free  electricity. 

For  illustration,  suppose  that  the  apparatus  is  in  the  condition 
represented  in  Fig.  320.  If  the  finger  be  touched  at  (7,  the  elec- 
tricity n  n  will  escape  to  the  earth  and  the  leaves  will  collapse.  The 
positive  charge  at  C  remains  bound  by  ^4's  charge.  If  now  A  be 
removed,  this  charge  will  diffuse  over  the  electroscope  and  the 
leaves  will  diverge  because  of  the  portions  which  they  receive. 

As  might  be  expected,  successive  inductions  may  be  obtained 
from  one  original  charge.  The  induced  charge  in  one  case  acts  as 
the  inducing  charge  in  a  new  induction. 

578.  Induction  Precedes  Attraction. — Whenever  a  body 
is  attracted  because  of  the  charge  of  electricity  on  another  body,  it 
is  always  subjected  to  induction  before  it  is  attracted. 


ELECTRICITY     AND     MAGNETISM. 


Thus,  if  B  (Fig.  321)  is  attracted  by  a  positive  charge  on  A, 
the  attraction  is  always  preceded  by  an  induction,  whereby  B  is 
charged  negatively  at  c  and  positively  at  d  ; 
c  is  nearer  than  d,  hence  the  attraction  be- 
tween a  and  c  is  greater  than  the  repulsion 
between  a  and  d.  Accordingly  attraction 
predominates. 

579.  Quantity  of  the  Induced  Elec- 
tricity.— The  total  quantity  of  electricity,  of 
the  opposite  kind  to  its  own,  which  a  charged 
body  induces  on  neighboring  bodies  is  ex- 
actly equal  to  its  own  charge.  This  was  experimentally  proved  by 
Faraday  by  means  of  an  "ice-pail."  A  metallic  pail,  A  (Fig.  322), 
was  mounted  upon  an  insulating  support.  The  outside  of  the  pail 
was  connected  with  a  delicate  electroscope.  Into 
this  pail  was  lowered  a  positively  charged  ball,  FIG.  322. 

B,  which  was  suspended  from  an  insulating  silk 
thread.  Upon  introducing  the  ball  the  leaves  of 
the  electroscope  commenced  to  diverge,  because 
the  charge  on  B  induced  negative  electricity  on 
the  interior  of  the  pail  and  held  it  bound.  The 
positive  electricity  of  the  pail,  being  free  and  re- 
pelled, passed  partly  into  the  electroscope.  As 
the  ball  was  lowered  further  the  leaves  diverged 
more  and  more  until,  after  a  certain  depth  had 
been  reached,  a  further  descent  produced  no 
extra  divergence.  Even  when  the  ball  was 
brought  into  contact  with  the  bottom  of  the  pail 
the  leaves  remained  undisturbed  and  extended. 
Upon  removing  the  ball,  after  contact,  the  charge 
was  found  to  have  disappeared  from  it.  The 
fact  that  the  gold-leaves  were  undisturbed  by  the  contact  of  the 
ball  with  the  pail  proves  that  there  was  the  same  quantity  of 
negative  electricity  on  the  inside  of  the  pail  as  positive  electricity 
on  the  ball.  Coming  together  the  two  neutralized  each  other  and 
left  the  positive  outside  charge  undisturbed. 

580.  Condensers. — If  a  pane  of  glass  be  taken,  and  a  piece 
of  tin-foil  be  pasted  upon  the  middle  of  each  face  of  the  pane,  and 
one  piece  be  charged  positively,  the  inner  surface  of  the  other 
piece  will  receive  a  negative  charge  by  induction.  If  the  second 
piece  be  connected  with  the  earth  positive  electricity  will  escape. 
The  positive  electricity  of  the  first  tin-foil  will  attract  and  hold  the 
negative  of  the  second  bound.  If  the  connections  to  the  source 


SPECIFIC    INDUCTIVE    CAPACITY.  365 

the  earth  be  now  removed,  it  will  be  found  that  hardly  any 
electricity  can  be  obtained  by  merely  touching  either  of  the  foils. 
It  may  be  said  that  each  charge  is  inducing  the  other.  It  will  be 
found  that  these  two  pieces  of  tin-foil  may  be,  when  thus  arrangedr 
much  more  strongly  charged  than  either  of  them  could  possibly 
be,  if  it  were  placed  alone  upon  a  piece  of  glass  and  then  elec- 
trified. In  other  words,  the  capacity  of  a  conductor  is  greatly 
increased  when  it  is  placed  near  to  a  conductor  electrified  with 
the  opposite  kind  of  charge.  Considering  then  (Art.  570)  that  the 

potential  V  =  -^>  it  will  be  seen  that  such  a  piece  of  apparatus 

L> 

can  receive  a  large  quantity  of  electricity,  Q,  without  raising  its 
potential,  V,  as  much  as  if  it  were  separated  from  all  conducting 
or  electrified  bodies.  Such  an  arrangement  is  called  a  con- 
denser. 

Condensers  are  much  used  in  practical  electricity  for  measur- 
ing quantities  of  electricity.  A  pane  of  glass,  however,  would  not 
have  a  sufficiently  large  capacity  for  technical  purposes.  Accord- 
ingly commercial  condensers  are  made  by  piling  together  alternate 
sheets  of  tin-foil  and  paraffined  paper.  The  alternate  layers  of 
tin-foil  are  connected  together.  In  this  manner  a  large  surface 
of  tin-foil  can  be  used  and  yet  not  occupy  an  inordinate  amount  of 
space.  The  capacity  of  a  condenser  varies  inversely  as  the  thick- 
ness of  the  dielectric  between  the  conducting  sheets,  and  directly  as 
the  product  of  the  area  of  the  sheets  and  a  constant  depending 
upon  the  nature  of  the  dielectric.  This  constant  is  called  the 
specific  inductive  capacity. 

581.  Specific  Inductive  Capacity, — It  has  been  stated  (Art. 
563)  that  a  body  charged  with  Q  units  of  electricity  will  attract  an 
unlike  unit  of  electricity  on  a  body  which  is  r  centimetres  away 
with  a  force 

F        Q 
~~^' 

This  is  strictly  true  only  when  the  two  bodies  are  in  a  vacuum. 
It  is  very  nearly  true  when  they  are  separated  from  each  other  by 
dry  air  or  any  other  gas.  That  the  expression  for  the  force  may 
be  universally  true,  whatever  be  the  dielectric  which  intervenes 
between  the  bodies,  it  must  be  modified  into  the  form 

F-^. 
~  Kr* 

Here  K  is  a  constant,  which  is  peculiar  to  each  substance,  and  it 
is  called  the  specific  inductive  capacity  or  the  dielectric  constant  of 
the  substance. 


366  ELECTRICITY    AND    MAGNETISM. 

The  following  is  a  table  of  specific  inductive  capacities  referred 
to  air  at  0°  C.  and  760  mm.  pressure  as  unity : 

Air  and  most  gases 1.0 

Bisulphide  of  Carbon 2.2 

Ebonite  and  Rubber 2.3 

Paraffin 2.3 

Shellac 2.9 

Sulphur 3.7 

Glass ...  3. 2  to  6.0 

Water 6.0 

Metals oc 

The  name  "inductive  capacity"  was  introduced  by  Faraday  in  the 
publication  of  a  series  of  experiments  upon  condensers.  He  con- 
structed a  number  of  exactly  similar  condensers,  differing  from 
each  other  only  in  the  dielectric  between  the  conducting  surfaces. 
The  dielectrics  which  he  used  were  air,  sulphur,  shellac,  and  glass. 
He  measured  the  capacities  of  these  equally  dimensioned  con- 
densers and  found  that  all  the  others  had  greater  capacities  than 
the  one  containing  air.  Remembering  that  induction  is  the  prin- 
ciple upon  which  the  condenser  works,  it  can  readily  be  seen  why 
Faraday  adopted  the  term. 

Modern  writers,  however,  in  employing  the  term  "dielectric 
constant "  indicate  their  appreciation  of  the  important  light  thrown, 
by  the  mere  existence  of  different  values  of  K,  upon  the  true 
nature  of  electricity.  The  fact  that  the  nature  of  the  substance 
between  two  charges  of  electricity  influences  the  magnitude  of 
their  repulsions,  disproves  the  idea  that  electrical  attractions  and 
repulsions  are  action  at  a  distance.  There  must  be  something  be- 
tween the  bodies  which  plays  a  part.  Again,  the  repulsion  of  two 
charges  of  electricity,  even  when  suspended  in  a  vacuum,  indicates 
that  this  something  must  be  the  ether.  The  ether,  then,  in  differ- 
ent dielectrics,  must  in  some  manner  be  modified  from  what  it  is 
in  a  vacuum.  This  is  known  to  be  the  case  from  the  different 
optical  properties  of  bodies. 

A  method  for  showing  directly  the  effect  of  K  in  Coulomb's  law 
has  been  constructed  by  Mayer.  Suspend  horizontally  a  silvered 
circular  disc  of  mica,  16  cms.  in  diameter,  by  a  long,  slender,  spiral 
spring.  Let  the  spring  be  in  contact  with  the  silvered  surface. 
Under  this  disc  place  another  of  metal,  which  is  movable  in  a 
vertical  direction,  and  is  connected  to  the  earth.  Charge  the 
silvered  mica  with  electricity,  using  the  spring  as  a  means  of 
connection.  If  the  distance  between  the  two  discs  is  but  two  or 
three  centimetres,  the  mica  will  be  attracted  so  as  to  extend  the 
spring.  If,  now,  a  sheet  of  paraffin  or  plate  of  glass  be  interposed 
between  the  two  discs,  the  attractive  force  will  be  observed  to 


LEYDEN    JAR.  367 

decrease.  This  is  because  K  in  the  denominator  of  the  fraction 
•expressing  the  force  of  attraction  is  greater  for  glass  and  paraffin 
than  for  air. 

It  will  be  noticed,  in  the  table  given,  that  K  for  metals  and 
•conductors  is  x.  According  to  this,  a  charged  body  cannot 
attract  a  pith-ball  through  a  metal  plate.  The  metal  is  therefore 
called  an  electric  screen.  The  screen  must  be  sufficiently  large  to 
prevent  any  attractive  force  from  working  around  its  edges,  and  it 
should  be  connected  with  the  earth  to  avoid  any  induced  electricity 
from  exerting  an  influence.  It  is  in  consideration  of  these  facts 
that  electrometers  are  surrounded  by  conducting  cages,  which  are 
connected  with  the  earth.  Any  neighboring  accidental  charges  of 
-electricity  cannot  then  influence  the  electrometer  needle. 

582.  Ley  den  Jar. — A  most  convenient  form  of  condenser, 
for  demonstrative  experiments,  is  the  Leyden  jar.     It  usually  con- 
sists (Fig.  323)  of  a  glass  jar  coated  up  to  a  certain  height  on  the 
inside  and  outside  with  tin-foil.     A  brass  knob  fixed 

on  the  end  of  a  stout  brass  wire  passes  downward  FlG- 
through  an  insulating  lid  and  is  connected  by  a  chain 
with  the  interior  coating  of  tin-foil.  To  charge  the  jar, 
it  is  held,  by  the  outer  coating,  in  the  hand,  and  the 
brass  knob  is  approached  to  any  source  of  electricity. 
If  the  source  furnishes  positive  then  the  internal  coat- 
ing becomes  charged  positively,  and  this  induces  and 
binds  an  equal  amount  of  negative  electricity  on  the 
outer  coating,  while  an  equal  amount  of  positive  will  be 
rendered  free  and  will  escape  through  the  hand  to  the 
ground.  The  jar  being  now  removed,  is  said  to  be 
charged — there  exists  a  state  of  positive  potential  on  the  inside  and 
negative  potential  on  the  outside.  Both  electricities  are  bound, 
and  neither  can  produce  effects  independently.  If,  however,  they 
be  allowed  to  come  in  connection  with  each  other  (by  joining  the 
outside  coating  and  the  ball  at  the  top  with  a  wire)  the  electricities 
rush  to  neutralize  each  other,  and  will  even  spark  across  an  air 
gap.  The  jar  is  then  said  to  be  discharged.  The  length  of  the 
air  gap  through  which  the  spark  will  pass  depends  upon  the  differ- 
ence of  potential  between  the  inner  and  outer  coatings.  Some- 
times the  difference  of  potential  becomes  so  great,  owing  to 
carelessness  in  charging,  that  the  electricities,  in  striving  to  get 
together,  will  pierce  and  fracture  the  glass  itself. 

583.  Seat  of  the  Charge.— If  a  jar  is  made  with  a  wide,  open 
top,  and  the  coatings  movable,  then,  after  charging  the  jar,  the 
coatings  may  be  removed  and  tested  without  showing  any  trace  of 


368  ELECTRICITY    AND    MAGNETISM. 

electricity  upon  them.  If  they  be  then  replaced,  the  jar  will  be 
found  to  be  charged  as  before  removal.  Benjamin  Franklin  in- 
ferred from  this  that  the  electricity  resides  upon  the  dielectric  and 
the  coatings  serve  only  to  readily  diffuse  the  charge  over  the  surface. 

584.  Residual  Charge. — If  a  jar  be  charged,  left  for  a  time, 
discharged,  and  left  for  a  while  longer,  it  will  be  found  that,  upon 
connecting  the  two  coatings,  a  spark  may  be  obtained.     The  elec- 
tricity remaining  in  the  jar  after  the  first  discharge  is  called  the 
residual  charge.     The  amount  of  residual  charge  varies  with  the 
time  that  the  jar  has  been  left  charged.     It  also  depends  upon 
the  kind  of  dielectric  used.     No  residual  charge  has  been  found 
in  connection  with  an  air-condenser. 

585.  Modern  Theory  of  Condensers. — The  modern  ether 
theory  of  electricity  gives  a  very  satisfactory  explanation  of  con- 
densers.    According  to  this  theory  electricity  is  the  ether  itself. 
When  a  conductor  is  statically  charged,  it  is  not  the  ether  of  the 
conductor  which  constitutes  the  charge,  but  the  ether  of  the  dielec- 
tric which  surrounds  the  conductor.     More  exactly,  charging  a 
conductor  is  straining  the  ether  particles  of  the  surrounding  dielec- 
tric out  of  a  definite  position,  which  they  are  presumed  to  have  a 
tendency  to  remain  in.     Thus,  if  a  positive  charge  is  communicated 
to  the  inner  coating  of  a  Leyden  jar,  the  ether  particles  of  the  glass 
will  all  be  strained  away  from  the  inside.     All  the  particles  will  be 
strained  away  from  the  inner  coating  and  toward  the  outer  coat- 
ing.    We  may  thus  say  that  the  inner  is  positively  electrified  and 
the  outer  negatively.     We  have  but  one  ether  electrification,  but 
two  ways  of  looking  at  it — just  as  a  dent  in  a  tin  plate  may  be  con- 
vex on  one  side  and  concave  on  the  other. 

In  all  dielectrics  the  ether  particles  are  supposed  to  be  held  in 
position  by  elastic  ties  of  some  sort.     A  mechanical  analogy  is  to- 
represent  the  particle  (Fig.  324)  by  a  bead  fastened  to  the  centre 
of  an  elastic  wire,  clamped  at  both  sides.     When 
FIG.  324.  subjected  to  an  electrifying  influence,  the  bead  is 

pulled  to  one  side.     Upon  releasing  the  bead,  or 
/  %  discharging  the  electricity,  two  things  are  to  be 

/     \  noticed.     First,  the  bead  will  not  only  go  back  to 

0  "4"     its  original  position,  but  will  go  beyond  it  and 
/  oscillate  a  number  of  times  before  coming  to  rest. 

According  to  this,  then,  the  spark,  at  discharging 
a  Leyden  jar,  should  be  oscillatory  and  made  up 
of  a  succession  of  small  sparks.     Such  is  the  case, 
as  has  been  shown  by  reflection  upon  a  screen  from  a  rapidly 
rotating  mirror.     Were  the  spark  a  continuous  one,  its  reflected 


HERTZ'S    EXPERIMENTS.  369 


image  would  appear  as  a  prolonged  line.  It  appears,  however,  as 
a,  dotted  line.  Secondly,  it  must  be  considered  that,  if  the  strain 
on  the  wire  be  maintained  for  any  length  of  time,  it  will  not,  upon 
release,  immediately  return  to  its  normal  position,  but  will  assume 
a  new  one,  which  is  displaced  in  the  direction  of  the  strain  from 
the  original  position.  This  is  a  common  phenomenon  and  is 
known  as  elastic  fatigue.  The  electrical  parallel  is  the  residual 
charge.  After  the  first  discharge  the  ether  particles  have  not 
returned  to  their  normal  position.  It  requires  one  or  more  resid- 
ual discharges  before  they  return  to  that  position. 

Of  course  in  a  dielectric  we  cannot  suppose  that  each  of  the 
infinite  number  of  particles  of  ether  is  supported  upon  anything 
similar  to  an  elastic  wire,  for  the  dielectric  would  act  well  in  one 
direction  and  not  at  all  in  the  direction  of  the  length  of  the  wire. 
'This  is  not  in  accordance  with  facts.  Accordingly  it  is  supposed 
that  the  dielectric  acts  as  a  mass  of  jelly,  in  which  its  ether  par- 
ticles are  suspended,  or  possibly  the  ether  is  a  jelly-like  mass  in 
itself,  lacking,  however,  the  physical  property  impenetrability. 
The  jelly  then  exerts  a  restraining  force  to  strains  exerted  in  any 
direction  upon  the  particles. 

Conductors,  on  the  other  hand,  are  supposed  to  exercise  little 
or  no  restraint  upon  the  free  movement  of  the  ether  within  them. 

Viewed  in  this  light,  when  a  positive  charge  is  communicated 
to  a  conductor,  an  attempt  is  made  to  force  more  ether  into  tho 
conductor  than  it  ordinarily  has.  But  the  ether  is  absolutely 
incompressible.  Hence  room  is  made  for  the  extra  amount,  by 
pressing  the  ether  of  the  dielectric  away  from  the  conductor.  The 
«xtra  ether  must  have  been  taken  from  somewhere,  and  the  place 
which  it  formerly  occupied  must  be  filled.  This  is  done  by  the 
distention  of  the  remote  portions  of  the  dielectric.  It  presses  out 
of  some  conductor  an  equal  amount  of  ether.  We  can  thus  see  the 
truth  of  Faraday's  statement  that  it  is  impossible  to  charge  one 
body  alone.  Whenever  a  body  is  charged  positively,  some  other 
body  or  bodies  must  receive  an  equaj  negative  charge. 

When  a  Leyden  jar  is  discharged,  by  connecting  the  two  coat- 
ings through  a  conductor,  the  ether  in  the  positive  coating  flows 
toward  the  negative  and  the  strain  on  the  dielectric  is  relieved. 
This  flow  will,  of  course,  be  vibratory,  owing  to  the  inertia  of  the 
dielectric  jelly. 

586.  Hertz's  Experiments. — Professor  Hertz  has  shown  ex- 
perimentally that  the  electrical  ether  is  wonderfully  like,  if  not  iden- 
tical with,  the  ether  presupposed  in  light.  By  rapidly  charging 
and  discharging  a  conductor  he  causes  the  ether  upon  it  to  surge 


370  ELECTRICITY    AND    MAGNETISM. 

to  and  fro.  This  agitates  the  surrounding  dielectric  ether,  and! 
the  disturbances  travel  in  waves.  The  velocity  of  propagation 
he  determines  to  be  the  same  as  the  velocity  of  light.  He  has 
made  these  waves  interfere,  has  reflected  them  from  metal  mirrors, 
refracted  them  through  lenses  and  prisms  of  pitch,  and  has  pro- 
duced diffraction  effects.  He  has  shown  that  many  optical  experi- 
ments can  be  electrically  performed  by  substituting  dielectrics  for 
transparent  and  conductors  for  opaque  bodies. 

587.  Electrical  Machines. — The  method  of  rubbing  sealing- 
wax  with  fur  is  too  slow  for  the  production  of  large  quantities  of 
electricity.     Franklin  improved  upon  this  method,  employing  a 
machine,  which  rotated  a  large  glass  cylinder,  the  cylinder  being 
rubbed  by  a  silk  rubber.     But,  at  present,  machines  which  gen- 
erate electricity  by  friction  are  little  used,  recourse  being  made 
instead  to  the  principle  of  induction.     Two  machines  of  this  sort, 
most  commonly  found,  are  the  electrophorus  and  the  Holtz  ma- 
chine. 

588.  Electrophorus. — The  electrophorus  consists  of  a  cir- 
cular cake  of  resin,  sulphur,  or  vulcanized  rubber  in  a  metallic 
base,  A  (Fig.  325),  and  a  metallic  disc,  B,  having  an  insulating 

FIG  325  handle.     Stroking  with  flannel  or  fur  elec- 

trifies the  resin  negatively.  This  induces 
and  binds  positive  electricity  on  the  lower 
face  of  the  disc,  when  placed  upon  it.  Free 
negative  is  repelled  to  the  upper  face.  If 
the  finger  be  touched  to  the  disc,  while  it 
yet  remains  upon  the  resin,  the  free  neg- 
ative will  escape  to  the  earth.  Upon  then 
lifting  the  disc  it  will  be  found  charged 
with  positive  electricity.  This  operation  may  be  repeated  in- 
definitely. 

589.  Holtz  Machine.— This  machine,  illustrated  in  Fig.  326, 
consists  of  a  revolving  glass  disc,  A,  and  a  stationary  glass  disc,  B, 
both  well  coated  with  shellac  to  further  insulation.     In  front  of  A, 
and  close  to  it,  as  shown  in  the  figure,  are  two  combs  connected 
with  the  discharging  knobs  at  G.     On  the  back  of  the  disc  B, 
opposite  to  the  combs,  are  two  paper  sectors,   a  paper  tongue 
or  point  from  each  projecting,  through  an  opening  (window)  in 
the  stationary  disc,  toward  the  revolving  plate.      If  a    plate  of 
vulcanite  be  excited,  and  then  be  laid  against  one  of  the  paper 
sectors,  while  the  disc  A  is  rapidly  rotated  toward  the  point  of  the- 
sectors,  the  discharging  knobs  being  in  contact,  electrical  induction. 


HOLTZ  MACHINE. 


371 


FIG.  326. 


•will  ensue,  and  after  a  few  moments  the  knobs  may  be  gradually 
separated  until  sparks  perhaps  12  or  20  inches  long  pass,  accord- 
ing to  the  size  of  the  ma- 
chine. To  produce  sparks 
of  great  density  two  Leyden 
jars,  D,  D,  with  their  inner 
coatings  connected  to  the 
discharging  knobs  and  their 
outer  coatings  connected  with 
each  other,  are  added. 

To  explain,  in  a  very  gen- 
eral way,  the  action  of  the 
machine,  let  A  (Fig.  327) 
represent  the  revolving  plate 
and  B  the  stationary  disc  be- 
hind it,  carrying  the  paper 
sectors  a  and  6.  Imagine 
the  combs  in  front  of  A,  and 
call  them  a  and  b  also,  re- 
membering that  the  sectors 
are  on  the  plate  B,  behind  A. 
If  now  a  positive  charge  be 
communicated  to  the  sector 
a,  it  will  act  inductively  upon 
the  comb  a,  through  the  re- 
volving plate,  as  a  dielectric.  Negative  electricity  will  be  induced 
in  the  comb,  and,  if  it  were  of  proper  shape,  would  be  bound. 
But,  being  pointed,  the  negative  charge 
escapes  to  the  surface  of  A  and  is  carried 
around  with  it.  The  positive  electricity 
of  the  comb  is  repelled  by  the  process  of 
induction  to  the  discharging  knob  con- 
nected with  it.  Both  knobs  being  in 
contact  it  passes  to  the  comb  b.  From 
here  it  escapes  to  the  front  of  the  revolv- 
ing disc,  and  at  the  same  time  induces 
negative  electricity  on  the  upper  portion 
of  the  sector  b.  Because  of  the  induction 
positive  electricity  escapes  from  the  point 
of  the  sector  b  to  the  back  of  the  revolv- 
ing disc.  If  now  the  disc  be  revolved  half-way  around,  the  pos- 
itive charge  on  the  back  of  A  will  be  taken  up  by  the  point  of 
sector  a,  thus  strengthening  its  original  charge.  Sector  b,  having 
now  become  charged  negatively  increases  the  flow  of  positive  from 


372  ELECTRICITY    AND    MAGNETISM. 

comb  6,  and  sector  a,  having  its  charge  increased,  still  further 
increases  this  flow.  All  the  arrangements  conspire  to  charge  both 
the  rear  and  front  of  the  upper  half  of  A  with  positive,  and  of  the 
lower  half  with  negative,  electricity.  The  action  requires  that 
positive  electricity  shall  flow  continuously  through  the  knobs 
from  a  to  b.  When  sufficient  potential  difference  between  the 
combs  has  been  obtained,  the  discharging  knobs  may  be  separated 
and  a  spark  will  rupture  the  air. 

The  Ley  den  jars  serve  to  increase  the  capacity  of  the  knobs,  and 
thus,  for  a  spark  at  a  given  potential  difference,  to  increase  the 
quantity  of  electricity  passed. 

A  modification  of  the  Holtz  machine  has  been  made  by  Wims- 
hurst.  The  two  plates,  furnished  with  numerous  sectors  of  tin- 
foil, are  rotated  in  opposite  directions.  A  full  description  is  out 
of  place  here. 

590.  Effects  of  Statical  Discharge. — Most  electrical  effects 
are  best  obtained  by  the  use  of  current  electricity.     Those  which 
require  the  high  potential  of  statical  electricity  are  the  following : 

MECHANICAL. — If  a  heavily  charged  Leyden  jar  be  made  to  dis- 
charge itself  through  a  piece  of  glass  or  card-board,  it  will,  by  the 
passage,  pierce  a  hole  through  the  piece.  In  case  card-board  is 
used,  it  will  be  found  that  there  is  a  burr  on  both  sides  of  the 
card.  This  is  because  of  the  vibratory  character  of  the  discharge. 

PHYSIOLOGICAL. — If  a  discharge  is  made  through  a  human  being, 
the  muscles  which  lie  along  its  path  will  be  strongly  contracted. 
Those  who  have  received  very  powerful  shocks  from  electrical 
discharges  say  that  the  feeling  is  as  though  all  the  muscles  had 
been  so  severely  contracted  as  to  result  in  spraining  them.  The 
action  of  the  electricity  is  through  the  medium  of  the  nerves. 

HEATING. — A  very  sudden  development  of  heat  accompanies  the 
spark  at  discharge.  This  can  be  easily  shown  by  allowing  a  spark 
to  pass  to  the  tip  of  a  gas-burner.  If  the  gas  be  turned  on,  it  will 
become  ignited.  If  gas  be  not  available,  the  spark  may  be  passed 
to  a  spoon  containing  a  few  drops  of  common  ether. 

591.  Lightning. — Water,  in   the   process  of   evaporation,   is 
supposed  to  become  electrified.     From  the  surface  of  large  bodies 
of  water  multitudes  of  small  electrified  particles  of  moisture  rise 
into  the  air,  under  the  influence  of  the  hot  sun.     These  particles 
have  a  definite  capacity  (their  radius)  and  a  definite  quantity  of 
electricitj'.     In   the   process   of    cloud   formation   these   particles 
come  into  drops.     Each  drop  receives  the  electricity  of  its  com- 
ponent particles  and  has  its  capacity  increased.     The  quantity  on 
the  drop  equals  the  sum  of  the  quantities  on  the  particles.     The 


MAGNETS.  373 

capacity  of  the  drop  is  less  than  the  sum  of  the  capacities  of  the 
particles.  Hence  the  potential  on  the  drop  is  greater  than  it  was 
upon  the  particles.  In  this  manner  clouds  are  formed,  having 
large  quantities  of  electricity  at  a  high  potential.  The  opposite 
kind  of  electricity  is  induced  in  the  earth,  and  the  air,  acting  as  a 
dielectric,  is  placed  under  severe  strain.  Eventually  the  strain 
becomes  too  great  and  the  air  gives  way.  The  equalization  of 
potential,  at  that  instant,  gives  what  is  termed  a  stroke  of  light- 
ning. The  intense  heat  developed  by  the  discharge  expands  the 
air,  and  the  rushing  of  cold  air  into  the  partial  vacuum,  thus 
formed,  produces  the  sound  thunder. 

Sheet  lightning,  where  a  large  surface  is  momentarily  illu- 
minated, is  but  the  reflection  from  a  cloud  of  an  invisible  true 
discharge. 


CHAPTER    III. 

MAGNETISM. 

592.  Natural   Magnets. — The  ancients  discovered  that  a 
certain  black  stone,  abundantly  found  in  Magnesia,  had  the  prop- 
erty of  attracting  to  it  small  pieces  of  iron.     Accordingly,  from 
their  source,  they  called  these  stones  magnets.     Afterwards  they 
found  that,  when  hung  by  threads,  a  certain  part  of  each  stone 
always  pointed  north.     From  this  property  the  stone  received  the 
name  Lodestone  (leading  stone). 

593.  Artificial  Magnets. — If  a  piece  of  steel  be  rubbed  with 
a  lodestone,  it  will  be  found  to  have  acquired  the  property  of 
attraction.      Steel   artificial   magnets  are  what  are  employed  in 
-experiments  in  the  laboratory. 

594.  Poles  of  a  Magnet. — If  a  steel-bar  magnet  be  rolled  in 
ironfilings(Fig.328), 

it  will   be   observed 

that   the  attractions 

seem    to    have    two 

common  sources,  two 

points  near  the  ends 

of  the  bar.     These  two  points  are  called  the  poles  of  the  magnet. 

The  straight  line  connecting  the  poles  is  called  the  magnetic  axis. 

595.  Magnetic  Needle. — For  investigating  the  attractions 


374 


ELECTRICITY    AND    MAGNETISM. 


FIG.  329. 


FIG.  330. 


of  magnets  use  is  made  of  the  magnetic  needle.     This  consists 
(Fig.  329)  of  a  light  steel  needle,  which  has  been  magnetized,  and,  by 

some  suitable  arrangement,  is  mounted 
upon  a  pivot.  It  is  capable  of  moving 
in  a  horizontal  plane  with  little  friction. 
Left  to  itself  it  will  assume  a  north  and 
south  direction.  That  end  of  it  which 
points  north  is  called  the  north  pole,  and 
the  other  end  the  south  pole.  The  com- 
passes sold  by  opticians  are  magnetic  needles,  whose  north  poles 
are  generally  more  pointed  than  their  south  poles. 

596.  Attractions  and  Repulsions. — If  a  piece  of  iron  be 
approached,  in  any  manner,   to  either  end   of  a  magnetic  nee- 
dle, the  needle  will  be  attracted  to- 
ward   the    iron.      The   same   result 

will  follow  if  either  end  of  a  magnet 
be  approached  to  an  iron  non-mag- 
netic needle.  However,  if  either  end 
of  a  magnet  be  approached  to  a  mag- 
netic needle  (Fig.  330)  attraction 
will  follow  when  the  adjacent  poles 
are  unlike,  and  repulsion  takes  place 
when  the  adjacent  poles  are  of  the 
same  kind.  Hence,  as  with  quan- 
tities of  electricity : 

Poles  of  the  same  name  repel,  and  those  of  contrary  name  attract 
each  other. 

597.  North  and  South  Poles  Inseparable.— If  any  one 
portion  of  a  piece  of  steel  be  touched  by  a  north  pole  of  a  lode- 
stone,  it  will  be  found  to  have  developed  a  south  pole.     At  the 
same  time,  however,  a  north  pole  has  been  developed  in  some 
other  part  of  the  steel.     Again,  if  a  bar  magnet  be  broken  at  a 
point  half-way  between  its  poles,  each  of  the  fragments  will  possess 
two  poles.     Successive  breaking  leaves  each  fragment  with  its  two 
different  poles.     The  end  of  a  fragment  which  had  a  pole  before 
the  rupture  retains  the  same  polarity  afterwards.    It  may  thus  be 
concluded  that  every  magnet  must  have  two  poles. 

598.  Magnetic  Induction. — When  a  bar  of  iron  is  brought 
near  to  the  pole  of  a  magnet,  though  attraction  is  the  phenomenon 
first  observed,  yet  it  is  readily  proved  that  this  attraction  results 
from  a  change,  which  is  previously  produced  in  the  iron.     Similar 
to  the  case  of  electrostatic  attraction,  the  iron  becomes  a  magnet 


COERCIVE    FORCE.  375 

by  induction  exerted  by  the  original  magnet.  By  moving  a  mag- 
netic needle  around  the  iron  it  will  be  found  that  the  end  of  the 
iron  which  is  placed  near  one  pole  of  the  magnet  becomes  a  pole 
of  the  opposite  name,  and  the  remote  end  a  pole  of  the  same  name. 
Hence  the  adjacent,  unlike  poles  of  the  iron  and  magnet,  attract 
each  other. 

The  induced  magnet  is  more  powerful  the  nearer  it  is  to  the 
inducing  magnet ;  it  is,  therefore,  greatest  when  the  two  bars  are 
in  contact. 

Soft  iron  retains  its  magnetic  properties  only  while  under  the 
influence  of  the  magnet.  Upon  removing,  it  will  be  found  to  have 
returned  to  its  neutral  state.  Had  steel,  or  impure  iron,  or  cast- 
iron  been  used,  it  would  have  been  found  to  have  retained  more  or 
less  of  the  magnetic  properties  caused  by  the  induction. 

The  inductive  action  may  be  well  seen  by  placing  iron  and 
magnet  upon  a  sheet  of  paper  and  then  sifting  iron-filings  upon 
them.  The  filings  will  attach  themselves  to  the  iron  in  the  same 
manner  as  to  the  magnet.  If  the  magnet  be  now  withdrawn,  the 
filings  around  the  iron  will  collapse,  showing  the. loss  of  magnetic 
polarity. 

The  induced  temporary  magnet  will,  in  its  turn,  induce  tem- 
porary magnetism  in  a  second  piece  of  iron,  and  this  again  in  a 
third  piece.  The  strength,  however,  decreases  as  the  pieces  get 
further  away  from  the  original  magnet. 

If  the  north  ends  of  two  equal  magnets  be  touched  to  the 
opposite  ends  of  a  bar  of  steel,  south  poles  will  be  induced  in  both 
ends  of  the  bar.  But  we  have  seen  that  every  south  pole  must 
have  a  north  pole  with  it.  Accordingly  examination  will  reveal 
that  the  bar  has  two  coincident  north  poles  at  its  middle.  Such 
intermediate  poles  are  termed  consequent  poles. 

599.  Retentivity  or  Coercive  Force. — The  extension  of 
the  experiment  of  breaking  a  magnet  (Art.  597)  leads  to  the 
inference  that  every  particle  of  steel  is  a  magnet  in  itself.  Before 
magnetization  these  molecular  magnets  point  in  all  directions,  and 
hence  exert  no  external  magnetic  influence.  Under  the  influence 
of  induction,  however,  these  are  made  to  assume  the  same  direc- 
tion. Fig.  331  gives  an  idea  of  the  probable  arrangement  of  a 
magnetized  piece  of  steel. 

The  shaded  ends  represent  FlG-  331. 

the  south  poles  of  the  mole- 
cular magnets.  When  they 
are  all  arranged  as  in  the 

figure  the  external  effect  is  as  though  there  were  a  south  pole  at  S> 
and  a  north  pole  at  N. 


376  ELECTRICITY     AND     MAGNETISM. 

Now  experiments  show  that  tempered  steel  is  much  more  diffi- 
cult to  magnetize  than  a  piece  of  soft  iron,  and,  after  being  once 
magnetized,  retains  its  magnetism  much  better.  It  is,  then,  rea- 
sonable to  suppose  that  the  existence  of  foreign  particles  (carbon) 
in  the  steel  hinders  and  clogs  the  turning  of  the  molecular  mag- 
nets from  their  chaotic  state  into  regular  arrangement.  Once 
arranged,  the  same  cause  prevents  a  disarrangement.  In  pure 
iron  the  hindrance  is  not  present.  This  resistance  against  a 
magnetizing  or  demagnetizing  force  is  called  retentivity  or  coercive 
force.  As  might  be  expected,  the  retentivity  is  modified  by  any- 
thing which  will  cause  the  molecules  to  vibrate,  as  hitting  sharp 
blows  with  a  hammer  or  heating  to  a  high  temperature.  A  magnet 
may  be  demagnetized  by  dropping  it  several  times  upon  the  floor. 

The  extreme  amount  of  magnetism  that  could  be  imparted  to  a 
bar  would  be  that  which  arranged  all  the  molecular  magnets  in 
the  same  direction.  The  magnet  is  then  said  to  be  saturated. 
After  removing  the  magnetizing  force,  however,  some  of  the  mole- 
cular magnets  would  of  their  own  accord  turn  from  line  and  others 
would  follow  their  example  in  time.  Hence  a  magnet  must  be 
kept  for  some  time  before  its  strength  can  be  considered  as 
constant.  Yet  a  constant  strength  may  be  obtained  by  "  cooking  " 
the  magnet.  It  is  saturated  and  then  placed  for  several  hours  in  a 
bath  of  steam,  removed  and  again  saturated  and  cooked.  Magnets 
treated  in  this  manner  are  said  to  remain  very  constant. 

600.  Law  of  Magnetic  Force.  —  Magnetic  attractions  and 
repulsions  take  place  according  to  a  law  similar  to  Coulomb's 
law  for  electrical  forces.  Two  like  isolated  magnetic  poles  of 
strengths  m  and  ra',  d  centimetres  from  each  other,  will  repel  each 
other  with  a  force  in  dynes, 


d* 

If  the  poles  were  different,  as  m  and  —  mr,  then  the  value  of  F 
would  be  negative.  A  negative  value  indicates  attraction,  and  a 
positive,  repulsion. 

The  magnetic  force  will  act  through  all  substances  except 
through  magnetic  substances,  i.e.,  those  which  are  attracted  by 
a  magnet.  No  attraction  can  take  place  through  a  large  iron 
sheet.  Such  a  piece  of  iron  is  called  a  magnetic  screen.  A  small 
magnet  suspended  in  a  hollow  iron  sphere  cannot  be  deflected  by 
an  outside  magnet. 

601.  Unit  Magnet  Pole.  —  If,  in  the  formula  for  the  force, 
given  in  the  previous  article,  F  and  d  be  supposed  each  equal  to 
unity,  then,  as  in  electrostatics  (Art.  563), 


LAMINATED     MAGNETS. 


37T 


The  unit  magnetic  pole  is  one  that  mil  repel  an  equal  like  polef 
when  at  a  unit's  distance,  with  a  unit  force. 

Of  course  an  isolated  pole  cannot  be  obtained,  for,  in  a  magnet,  it 
is  always  accompanied  by  an  opposite  equal  pole,  and  the  algebraic 
sum  of  the  strengths  of  the  poles  of  a  magnet  always  equals  zero. 

The  poles  of  a  bar  magnet  are  the  points  from  which  all  the- 
forces  may  be  considered  to  emanate.  If  the  strength  of  one  of 
these  poles  be  multiplied  by  the  distance  between  the  two  poles,  a 
quantity  results  which  is  termed  the  magnetic  moment  of  the  bar. 
In  ordinary  bar  magnets  the  pole  distance  is  about  f  of  the  total 
length  of  the  bar. 

The  magnetic  moment  of  a  bar  divided  by  its  weight  in  grams 
gives  the  specific  magnetism  of  the  substance  of  which  the  bar  is  com- 
posed.    This  is  greatest  in  very  hard-tempered  steel. 
The  magnetic  moment  divided  by  the  volume  of  a 
magnet,  i.e.,  the  magnet  strength  per  unit  volume, 
is  termed  the  intensity  of  magnetization  and  is  gen- 
erally represented  by  the  letter  I. 

602.  Lifting  Power. — The  strength  of  a  mag- 
net must  not  be  confounded  with  its  lifting  power. 
The  latter  depends  upon  the  shape  of  the  magnet 
and  also  upon  the  shape  of  the  body  lifted.     A  mag- 
net bent  into  the  shape  of  a  horseshoe  (Fig.  332) 
will  lift  about  four  times  what  it  would  with  one 
end,   if   straight.     The   lifting   power   of  a   magnet 
grows  very  curiously,  if  the  load  be  gradually  in- 
creased from  time  to  time. 

603.  Laminated   Magnets. — Long,  thin  steel 
magnets  are  more  powerful  in  proportion  to  their 
weight  than  thicker  ones.     Hence  compound  mag- 
nets are  constructed,  consisting  of  thin  laminae  of 

steel  separately  magnetized  and  afterwards  bound  together  in 
bundles.  These  laminated  magnets  (Fig.  333)  are  more  powerful 

than  simple  bars  of  steel. 
The  explanation  of  this 
fact  seems  to  be  that 
ordinary  steel  magnets 
are  never  saturated,  and 

what  magnetism  they  have  results  from  molecular  arrangements 
near  the  surface.  The  compound  magnets  have  a  greater  surface 
and  are  hence  stronger.  Since  the  mutual  action  of  the  like  poles 
in  juxtaposition  tends  to  weaken  them,  the  strength  of  a  compound 
magnet  will  never  equal  the  sum  of  the  strengths  of  its  parts. 


FIG.  333. 


378 


ELECTRICITY    AND    MAGNETISM. 


That  the  magnetism  of  ordinary  bars  is  confined  to  the  surface 
has  been  shown  by  placing  the  magnet  in  acid  and  dissolving 
its  surface.  After  removal,  the  bar  showed  very  little  magnetic 
polarity. 

604.  Magnetic  Field. — Lines  of  Force.— The  space  around 
a  magnet  where  its  action  is  felt  is  termed  the  field  of  the  magnet. 
When  several  magnets  are  near  to  each  other  each  one  furnishes 
its  own  field,  and  superposed  upon  each  other  they  form  a  result- 
ant field. 

The  field  is  supposed  to  be  permeated  by  magnetic  lines  of 
force.     These  lines  represent  the  direction  along  which  the  mag- 
netic attractions  and 

FIG.  334.  repulsions    act.      An 

isolated  magnetic 
pole  would  move 
along  one  of  these 
lines  under  the  at- 
traction exerted  by 
the  field  magnet.  The  general  direction  of  the  lines  of  force  of  a 
bar  magnet  are  represented  in  Fig.  334. 

The  properties  of  these  lines  can  be  best  discussed  by  con- 
sidering only  those  which  lie  in  a  given  plane  passing  through  the 
magnet.  Such  a  section  is  called  a  magnetic  spectrum.  The  spec- 
trum may  be  graphically  represented  by  placing  a  sheet  of  white 
paper  over  a  magnet  and  then  sifting  fine  iron-filings  upon  the 
paper.  A  slight  tapping  on  the  paper  will  cause  the  filings  to 
arrange  themselves  along  the  lines  of  force,  as  represented  in 

FIG.  335. 


Fig.  335.  With  a  sufficiently  large  figure  it  would  be  seen  that 
every  line  starting  from  one  pole  finds  its  way,  by  a  curved  path, 
to  the  other  pole. 


MAGNETIC    FIELD.  379 

An  isolated  north  magnetic  pole,  placed  upon  one  of  these 
lines,  would  travel  along  it  away  from  the  north  pole  of  the  field 
magnet  and  toward  the  south  pole.  An  isolated  south  pole  would 
move  in  an  opposite  direction.  For  many  reasons  it  is  desirable 
to  direct  the  lines.  Hence,  as  represented  in  Fig.  334,  the  direc- 
tion which  an  isolated  north  pole  would  move  is  taken  as  the 
positive  direction. 

Of  course  it  is  impossible  to  get  an  isolated  pole,  but  the  unde- 
sired  companion  can  be  so  far  removed  as  not  to  interfere  with 
demonstrative  experiments.  If  a  shallow  glass  dish,  containing  a 
little  water,  be  placed  over  the  magnet  and  spectrum  shown  in  Fig. 
335,  and  then  a  magnetized  sewing-needle  be  floated  in  a  vertical 
position,  by  means  of  a  small  cork,  the  lower  pole  of  the  needle 
will  be  so  much  nearer  the  magnet  than  the  upper  pole  that  it  will 
act  as  an  isolated  pole.  When  placed  over  any  line  it  will  move 
along  that  line,  however  circuitous,  until  it  reaches  the  pole  of  the 
field  magnet,  which  attracts  it.  This  experiment  is  much  more 
satisfactory  when  the  field  magnet  is  an  electro-magnet.  The 
needle  may  then  be  placed  at  any  desired  point  and  commences 
to  move  only  after  the  magnet  is  excited.  Professor  Spice  sifts,  the 
filings  upon  a  glass  plate  and  projects  the  whole  experiment  from 
a  vertical  lantern. 

If  a  short  magnetic  needle  be  moved  around  a  field  whose  lines 
of  force  are  graphically  shown  by  iron-filings,  the  needle  will  turn 
until  its  magnetic  axis  coincides  with  the  direction  of  the  lines  of 
force.  In  fact  the  filings  themselves  are  little  magnets,  made  so 
by  induction,  and  tapping  the  paper  upon  which  they  rest  serves 
the  stead  of  a  pivot.  That  the  needle  should  so  place  itself  is 
quite  natural,  for  its  north  end  tends  to  travel  in  one  direction 
and  its  south  end  in  an  opposite  direction.  The  result  is  a  couple, 
which  turns  the  needle  until  the  pulls  are  from  the  same  line  of 
force,  passing  through  the  pivot. 

605.  Theory  of  the  Curvature  of  the  Lines.— In  any 

plane  passing  through  a  magnet,  N,  S  (Fig.  336),  let  P  be  an 
isolated  unit  north  pole.  Assume  its  distance  from  the  north 
pole  PN,  to  be  twice  as  great  as  from  the  south  pole  PS.  The 
unit  will  be  repelled  by  the  north  pole  with  a  certain  force,  which 
is  represented  in  amount  and  direction  by  the  line,  PB.  Then, 
according  to  the  law  of  magnetic  force  (Art.  600),  the  attraction 
exerted  by  the  south  pole,  which  is  only  half  as  far  away,  will  be 
four  times  as  great,  and  is  represented  in  magnitude  and  direc- 
tion by  the  line  A  P.  The  resultant  of  these  two  forces  must 
be  the  diagonal,  EP,  of  the  completed  parallelogram,  and  the 


3SO 


ELECTRICITY    AND    MAGNETISM. 


unit  pole  would  move  along  the  line  EP.     If  elementary  paral- 
lelograms be  constructed  in  this  manner  throughout  the  field, 

FIG.  336. 


their  diagonals,   when   connected,   will    represent    the    lines    of 
force. 

The  curvature,  then,  is  the  result  of  combined  attraction  and 
repulsion.  The  lines  of  magnetic  force  from  an  isolated  pole 
would  be  straight,  as  are  the  lines  along  which  gravitation  acts, 
and  the  law  given  in  Art.  600  is  true  for  isolated  poles  only. 

606.  Fields  from  Several  Magnets. — When  several  mag- 
nets are  in  the  same  vicinity,  the  resultant  field,  compounded 
from  the  separate  fields  of  each  magnet,  is  sometimes  curiously 

arranged.      Thus    the   field 

IG>  337*  from    two   magnets,    whose 

north  and  south  poles  are 
opposed  to  each  other,  is 
represented  in  Fig.  337. 
A  short  magnetic  needle 
would  be  in  stable  equi- 
librium if  placed  in  any 
part  of  this  field.  Fig.  338  shows  quite  a  different  field  where 
the  opposed  poles  are  like  named.  A  needle  moved  about  this 
field  would  suddenly  turn 
half  round  on  its  axis  at 
the  moment  of  crossing  the 
line  cd.  When  the  pivot 
is  exactly  upon  cd,  the 
needle's  south  pole  is  at- 
tracted equally  in  opposite 
directions  by  the  two  ex- 
posed north  poles.  In  the  same  manner  its  north  pole  is  repelled.. 


FIG.  338. 


STRENGTH    OF    THE    FIELD.  381 

The  result  is  that  the  needle  places  itself  so  that  its  axis  is  per- 
pendicular to  the  axis  of  the  field  magnets. 

Much  may  be  learned  by  experimenting  with  iron  filings  on 
variously  compounded  fields. 

607.  Strength  or  Intensity  of  Magnetic  Field.  —  It  may 

be  reasonably  supposed  that  each  line  of  force  exerts,  along  its 
length,  a  given  amount  of  force.  Hence  a  piece  of  iron,  which 
was  traversed  by  several  lines,  would  be  more  powerfully  attracted 
than  if  traversed  by  a  fewer  number.  Thus  a  magnet  pole  of 
definite  size,  placed  near  to  the  pole  of  the  field  magnet,  would  be 
attracted  with  more  force  than  at  a  distance,  for  the  lines  are 
closer  together  near  the  poles  of  the  field  magnet.  The  number 
of  lines  of  force,  then,  which  penetrate  a  given  area,  determines 
the  relative  force  exerted  by  the  field  at  that  place.  This  is  termed 
the  strength  or  intensity  of  the  field. 

In  order  to  compare  the  strengths  of  different  fields,  it  is  neces- 
sary to  have  a  unit  of  strength.  Hence 

A  magnetic  field  of  unit  strength  is  one  which  exerts  a  unit  force 
(dyne)  upon  a  free  unit  magnet  pole. 

608,  Determination  of  the  Strength  of  a  Field.—  If  a 

magnet,  suspended  by  a  fibre,  be  placed  in  magnetic  fields  of 
different  strengths,  it  will  oscillate  for  a  long  time,  and  the  times 
of  oscillation  will  be  shorter  the  stronger  the  field.  This  is  paral- 
lel to  the  case  of  pendulum  vibrations.  The  pendulum  vibrates 
because  of  the  force  exerted  by  gravity  and  because  of  its  inertia. 
Gravity  pulls  its  centre  of  gravity  as  near  as  possible  to  the  earth, 
and  inertia  carries  it  beyond  this  position.  If  the  force  of  gravity 
were  increased,  the  pendulum  would  vibrate  quicker.  In  the  case 
of  a  magnet,  the  force  of  the  field  takes  the  place  of  gravity. 
Now,  just  as  the  force  of  gravity  can  be  measured  by  the  time  of 
oscillation  of  a  given  pendulum  (Art.  163),  so  the  strength  of  a 
magnetic  field  can  be  measured  by  the  time  of  oscillation  of 
a  given  magnet. 

If  t  =  the  time  taken  by  the  magnet  in  passing  from  one 
turning-point  to  the  other  in  an  oscillation,  K  =  the  moment  of 
inertia  of  the  magnet  (Art.  160),  M  =  the  magnetic  moment  of  the 
magnet,  then  the  strength  of  the  field 

&=**. 

f  M 

When  the  same  magnet  is  used  K  and  M  are  constant,  hence 


, 
where  n  =  the  number  of  single  vibrations  in  a  second.     Then  if 


382  ELECTRICITY     AND     MAGNETISM. 

a  given  magnet  vibrates  n  and  ri  times  per  second  in  two  fields  of 
strengths  H  and  H', 


If  the  values  of  M  and  K  are  known  or  determined,  then  the  first 
equation  gives  the  absolute  strength  of  the  field,  provided  all  the 
quantities  are  expressed  in  proper  units. 

609.  Hysteresis.  —  If  a  piece  of  iron  be  placed  in  a  magnetic 
field,  it  will  have  two  opposite  poles  induced  in  it  wrhose  strengths 
depend  upon  the  strength  of  the  field.     If  the  strength  of  the 
field  be  vajied  from  zero  to  a  maximum,  and  then  to  zero  again, 
there  will  be  two  times  when  'the  field  will  have  a  definite  strength 
—  once  when  the  field  is  growing  stronger  and  again  when  it  is 
decreasing  in  strength.     The  strengths  of  the  induced  poles  in  the 
iron  are  different  in  these  two  equal  fields.     They  will  be  less  in 
the  increasing  field  than  in  the  decreasing.     The  strength  of  the 
iron's  poles  depends  upon  the  iron's  previous  history.     The  iron 
has  a  tendency  to  remain  in  its  previous  condition  and  behind  the 
field's  requirements.     This  peculiarity  of  the  iron  is  termed  by 
Ewing  static  hysteresis. 

If  iron  be  placed  in  a  magnetic  field  of  constant  strength,  it 
will  require  a  certain  time  before  its  induced  poles  assume  con- 
stant strengths.  To  this  property  "of  the  iron  Ewing  gives  the 
name  viscous  hysteresis. 

610.  Number  of  Lines  of  Force  from  a  Given  Pole.  —  It 
is  convenient  to  consider  the  number  of  lines  of  force  passing 
through  a  given  area  in  a  field  as  the  measure  of  the  strength  of 
the  field.     Each  line  may  be  supposed  to  exert  a  dyne  of  force  on 
a  unit  pole  pierced  by  it.     The  given  area  is  a  square  centimetre 
and  is  placed  so  as  to  l?e  perpendicular  to  the  lines  of  force.     A 
unit  field  would  then  have  one  line  passing  through  a  square  centi- 
metre. 

Suppose  now  that,  around  a  unit  magnet  pole,  we  conceive  a 
spherical  shell  of  one  centimetre  radius.  From  the  definition  of  a 
unit  pole  (Art.  601)  we  know  that  the  enclosed  pole  exerts,  on 
another  unit  pole,  a  dyne  of  force  at  every  point  on  this  shell. 
The  strength  of  the  field,  then,  at  all  these  points,  is  unity.  Hence 
every  centimetre  of  it  is  pierced  by  one  line  of  force.  But  the 
whole  .surface  of  the  sphere  of  unit  radius  contains  4  TT  centi- 
metres. The  unit  pole,  therefore,  sends  off  4  TT  lines  of  force.  An 
enclosing  surface  of  any  size  would  be  pierced  by  the  same  number 
of  lines. 


MAGNETIC    SUSCEPTIBILITY. 


3S3 


If  the  strength  of  the  pole  were  2  units,  it  would  send  off  8  TT 
lines  ;  or,  in  general, 

A  magnet  pole,  of  strength  m,  sends  out  4  TT  m  lines  of  force. 
This  conception  of  the  magnetic  lines  has  recently  developed  into 
many  important  theoretical  conclusions,  which  have  equally  im- 
portant practical  applications. 

With  a  real  magnet,  having  two  poles,  it  is  important  to  re- 
member that  the  lines  of  induction,*  starting  out  from  one  pole, 
finally  arrive  at  the  other  pole  and  thence  pass  through  the  magnet 
itself.  Hence  the  number  passing  through  a  section  of  the  mag- 
net lying  midway  between  the  poles  is  4  TT  m. 


611.  Magnetic  Susceptibility. — If  two  magnets,  with  their 
opposite  poles  opposed  to  each  other,  be  arranged  along  a  common 
axis,  and  if  the  lines  of  induction  be  made  visible  by  iron-filings,  the 
resulting  spectrum  will  be  as  in  Fig.  339.  If,  now,  a  piece  of  iron 


FIG.  339. 


FIG.  340. 


is  placed  between  the  poles,  the  field  alters  and  will  give,  e.g.,  the 
spectrum  shown  in  Fig.  340.  The  lines  are  much  more  numerous 
where  the  iron  is  than  they  were  before  it  was  placed  there.  Had 
a  piece  of  brass  been  used  instead  of  iron,  the  field  would  have 
remained  unclistorted.  A  piece  of  cobalt  would  have  produced 
some  distortion,  but  not  as  much  as  the  iron. 

The  cause  of  the  additional  lines  is  that  the  iron  has,  under  the 
influence  of  the  field,  become  an  induced  magnet  and  has  added 
its  lines  to  those  already  in  the  field. 

If  the  field  magnets  were  made  stronger,  they  would  send  out 
more  lines,  and  the  iron  would  become  more  strongly  magnetized 
and  would  also  send  out  more  lines.  Thus,  supposing  that  the 
iron  does  not  become  saturated,  the  strength  of  its  pole  depends 
upon  the  strength  of  the  field  and  upon  the  volume  of  the  iron. 
Suppose  that  the  strength  of  the  induced  pole  of  a  rectangular 
prism  of  iron  is  m;  that  the  pole  length  equals  the  physical 


*  A  line  of  induction  differs  from  a  line  of  force  in  that  it  does  not  change 
:its  direction  on  its  return  through  the  body  of  the  magnet. 


384  ELECTRICITY     AND     MAGNETISM. 

length  of  the  iron,  I;  that  the  cross-section  of  the  iron  is  s.  Ther* 
the  intensity  of  magnetization  (Art.  601) 

.  _  m  I        m 
s  I  ~  '   s 

If  the  cross-section  s  be  one  centimetre,  then  I  =  m,  or  the  inten- 
sity of  magnetization  is  equal  to  the  strength  of  the  induced  pole. 
It  has  been  found  that  if  the  strength  of  the  field  equals  H, 

I  =&H, 

where  k  is  a  constant  called  the  magnetic  susceptibility.  It  depends 
upon  the  kind  of  iron  or  other  substance  placed  in  the  field.  For 
iron,  nickel,  and  cobalt  the  value  is  positive ;  for  vacuum,  air,  and 
most  gases  is  practically  zero,  and  for  bismuth,  antimony,  and 
phosphorus  it  is  negative,  though  extremely  small. 

612.  Magnetic  Permeability. — In  almost  all  of  the  practical 
problems  on  magnetic  induction  it  is  desirable  to  know  the  total 
number  of  lines  which  pass  through  the  iron  suffering  induction. 
In  the  iron  prism  of  the  preceding  article  the  total  number 
traversing  it  is  made  up  of  two  parts :  4  TT  I  =  4  IT  k  H  lines  from 
the  induced  pole  and  H  lines  from  the  original  field.  Represent- 
ing this  sum  by  B,  we  have 

B  =  H  +  47T&H 

=   (1    +    4   7T  k)    H. 

It  is  customary  to  place  1  +  4  TT  k  =  /*,  whence 

B  =  ^H. 

Since  /*  involves  k,  it  depends  upon  the  character  of  the  substance 
under  induction.  For  air  and  gases  it  is  unity;  for  iron,  etc.,, 
greater  than  unity  (sometimes  reaching  16,000),  and  for  bismuth,, 
etc.,  less  than  unity. 

As  B  represents  the  number  of  lines  that  pass  through  a  square 
centimetre  of  iron,  and  H  the  number  through  air,  then  the  iron 
may  be  said  to  conduct  magnetic  lines  //,  times  better  than  air. 
From  consideration  in  this  light  //.  has  received  the  name  magnetic 
permeability. 

The  magnetic  permeability  of  a  substance  is  its  relative  con- 
ductivity for  magnetic  lines  of  force  as  compared  with  vacuum  (or 
air)  as  a  standard. 

The  equations  connecting  B,  H,  I,  /*,  and  k,  which  have  beem 
given  are  true  whatever  be  the  cross-section  of  the  iron  under 
induction.  The  assumption  of  a  square  centimetre  cross-section 
is  for  simplification  only. 

613.  The  Magnetic  Circuit. — In  the  construction  of  most 
electro-magnetic  apparatus  it  is  of  utmost  importance  that  as  much 
as  possible  of  the  field  of  the  magnetizing  agent  shall  be  occupied  by  a 


DIAMAGNETISM.  385 

substance  of  great  permeability  such  as  iron.  For  instead  of  having 
merely  the  lines  which  can  be  sent  through  air  by  the  agent  we 
can  just  as  well  have  the  additional  ones  from  the  iron.  Of  course 
an  air  gap  must  be  left  somewhere  in  the  circuit  of  the  lines  in 
order  to  introduce  the  body  to  be  acted  upon.  But  this  gap 
should  be  as  small  as  possible  if  a  maximum  effect  be  desired. 

If  the  opposite  poles  of  two  straight  electro-magnets  be  caused 
to  attract  a  piece  of  iron,  the  iron  fills  in  one  gap,  but  the  lines 
from  the  other  ends  pass  through  the  air.  The  force  of  the 
original  attraction  would  be  much  increased  if  the  extreme  ends 
were  connected  by  an  iron  bar.  This  last  bar  sends  its  additional 
lines  through  the  magnets  and  increases  the  force. 

614.  Paramagnetism  and  Diamagnetism.  —  Substances 
'which  have  a  permeability  greater  than  1  (that  of  vacuum)  as  iron, 
steel,  nickel,  cobalt,  etc.,  are  attracted  by  a  magnet  and  tend  to 
move  toward  it.  If  not  allowed  to  move  toward,  but  allowed  to 
rotate,  they  will  tend  to  set  themselves  axially  with  the  lines  of 
induction.  These  are  called  paramagnetic  substances. 

Substances  of  permeability  less  than  unity  show  the  opposite 
tendencies.  They  are  repelled  by  magnets  and  set  themselves 
perpendicular  to  the  lines  of  force.  They  are  bismuth,  antimony, 
phosphorus,  etc.  Without  making  use  of  the  term  permeability 
we  may  say : 

Those  substances  which  are  attracted  by  a  magnetic  pole,  or  which 
in  a  magnetic  field  tend  to  move  from  places  of  less  to  places  of 
-greater  intensity,  are  called  Paramagnetic. 

Those  substances  which  are  repelled  by  either  pole  indifferently, 
•or  which  move  from  ^places  of  greater  intensity  to  places  of  less 
intensity  in  the  field,  are  called  Diamagnetic. 

In  order  to  explain  the  phenomena  of  paramagnetism  and  dia- 
magnetism  we  have  to  consider  that  the  movable  parts  of  a  mag- 
netic circuit  strive  to  adjust  themselves  so  that  the  maximum  lines 
of  induction  shall  pass  through  the  circuit.  Paramagnetic  sub- 
stances are  thus  drawn  into  the  circuit  and  place  themselves 
longitudinally  with  the  lines,  while  diamagnetic  substances  act 
in  an  opposite  manner,  the  air  furnishing  more  lines  than  if  they 
should  displace  it. 

The  repulsion  of  diamagnetic  substances  is  hard  to  illustrate 
before  a  large  audience.  A  huge  electro-magnet  may  be  made  to 
slightly  repel  a  piece  of  bismuth  suspended  on  a  long,  delicate 
fibre.  Better  results  can  be  obtained  by  approaching  a  large 
piece  of  bismuth  to  one  of  the  needles  in  an  astatic  magnetom- 
eter (Art.  G25). 


386 


CHAPTER   IY. 

TERRESTRIAL     MAGNETISM. 

615.  The   Earth  a  Magnet.— If  a  needle  is  carried  round! 
the  earth  from  north   to  south,  it  takes  approximately  all  the 
positions  in  relation  to  the  earth's  axis  which  it  assumes  in  rela- 
tion to  a  magnetic  bar,  when  carried  round  it  from  end  to  end. 
At  the  equator  it  is  nearly  parallel  to  the  axis,  and  it  inclines 
at  larger  and  larger  angles   as  the   distance  from  the   equator 
increases ;  and  in  the  region  of  the  poles  it  is  nearly  in  the  direc- 
tion of  the  axis.     The  earth  itself,  therefore,  may  be  considered  a 
magnet,  since  it  affects  a  needle  as  a  magnet  does,  and  also  induces 
the  magnetic  state  on  iron.     But  it  is  necessary,  on  account  of  the 
attraction  of  opposite   poles,  to  consider   the   northern   part   of 
the  earth  as  being  like  the  south  pole  of  a  needle,  and  the  south- 
ern part  like  the  north  pole. 

616.  Declination   of   the    Needle.  — When  the  needle  is 
balanced  horizontally,  and  free  to  revolve,  ;t  does  not  generally 
point  exactly  north  and  south ;  and  the  angle  by  which  it  deviates 
from  the  meridian  is  called  the  declination.     A  vertical  circle  coin- 
cident with  the  direction  of  the  needle  at  any  place  is  called  the 
magnetic   meridian.      As   the   angle    between    the   magnetic   and 
the    geographical   meridians   is   generally   different   for   different 
places,  and  also  varies  at  different  times  in  the  same  place,  the 
word  variation  expresses  these  changes  in  declination,  though  it 
is  much  used  as  synonymous  with  decimation  itself. 

The  force  which  causes  the  needle  to  set  in  the  magnetic 
meridian  is  merely  directive. 

If  the  needle  be  weighed  before  it  is  magnetized  and  again 
after  it  has  been  made  a  magnet,  no  change  of  weight  can  be 
detected,  proving  that  the  earth's  attraction  for  one  pole  is  exactly 
equal  to  its  repulsion  of  the  other.  This  may  also  be  shown  by 
attaching  a  magnet  to  a  cork  and  thus  floating  it  upon  water.  It 
will  set  in  the  magnetic  meridian  but  will  show  no  tendency  to 
move  across  the  water  toward  the  north,  nor  in  any  other  direc- 
tion. This  effect  is  due  to  the  earth's  uniform  magnetic  field. 
The  magnetic  pole  of  the  earth  being  practically  at  an  infinite 
distance,  the  forces  of  attraction  and  repulsion,  being  equal,  con- 
stitute a  couple. 

617.  Isogonic  Curves. — This  name  is  given  to  a  system  of 
lines  imagined  to  be  drawn  through  all  the  points  of  equal  decli- 


ISOGONIC    CURVES. 


387 


nation  on  the  earth's  surface.  We  naturally  take  as  the  standard 
line  of  the  system  that  which  connects  the  points  of  no  declina- 
tion, or  the  isogonic  of  0°  (Fig.  341).  Commencing  at  the  north 

FIG.  341. 


pole  of  dip,  about  Lat.  70°,  Lon.  96°,  it  runs  in  a  general  direc- 
tion E.  of  S.,  through  Hudson's  Bay,  across  Lake  Erie,  and  the 
State  of  Pennsylvania,  and  enters  the  Atlantic  Ocean  on  the  coast 
of  North  Carolina.  Thence  it  passes  east  of  the  West  India 
Islands,  and  across  the  N.  E.  part  of  South  America,  pursuing  its 
course  to  the  south  polar  regions.  It  reappears  in  the  eastern 
hemisphere,  crosses  Western  Australia,  and  bears  rapidly  westward 
across  the  Indian  Ocean,  and  then  pursues  a  northerly  course 
across  the  Caspian  Sea  to  the  Arctic  Ocean.  There  is  also  a 
detached  line  of  no  declination,  lying  in  eastern  Asia  and  the 
Pacific  Ocean,  returning  into  itself,  and  inclosing  an  oval  area  of 
40°  N.  and  S.  by  30°  E.  and  W.  Between  the  two  main  lines  of 
no  declination  in  the  Atlantic  hemisphere,  the  declination  is  west- 
ward, marked  by  continued  lines  in  Fig.  341 ;  in  the  Pacific 
hemisphere,  outside  of  the  oval  line  just  described,  it  is  eastward, 
marked  by  dotted  lines.  Hence,  on  the  American  continent,  in 
all  places  east  of  the  isogonic  of  0°,  the  north  pole  of  the  needle 
declines  westward,  and  in  all  places  west  of  it,  the  north  pole 
declines  eastward;  on  the  other  continent  this  is  reversed,  as 
shown  by  the  figure. 

Among  other  irregularities  in  the  isogonic  system,  there  are 
two  instances  in  which  a  curve  makes  a  wide  sweep,  and  then 
intersects  its  own  path,  while  those  within  the  loop  thus  formed 
return  into  themselves.  One  of  these  is  the  isogonic  of  8°  40'  E., 
which  intersects  in  the  Pacific  Ocean  west  of  Central  America; 
the  other  is  that  of  22°  13'  W.,  intersecting  in  Africa. 


388  ELECTRICITY    AND    MAGNETISM. 

In  the  northeastern  part  of  the  United  States  the  declination 
has  long  been  a  few  degrees  to  the  west,  with  very  slow  and 
somewhat  irregular  variations. 

618.  Secular   and    Annual   Variation.  —  The    decimation 
of  the  needle  at  a  given  place  is  not  constant,  but  is  subject  to  a 
slow  change,  which  carries  it  to  a  certain  limit  on  one  side  of  the 
meridian,  when  it  becomes  stationary  for  a  time,  and  then  returns, 
and  proceeds  to  a  certain  liinit  on  the  other  side  of  it,  occupying 
two  or  three  centuries  in  each  vibration.     At  London,  in  1580,  the 
declination  was  11£°  E. ;  in  1657,  it  was  0° ;  after  which  time  the 
needle  continued  its  western  movement  till  1818,  when  the  decli- 
nation was  24^-°   W. ;    since   then   the  needle   has  been  moving 
slowly  eastward,  and  in  1879,  at  Kew,  the  declination  was  19° 
7'  west. 

The  entire  secular  vibration  will  probably  last  more  than  three 
centuries.  The  average  variation  from  1580  to  1818  was  9'  10" 
annually.  But,  like  other  vibrations,  the  motion  is  slowest  to- 
ward the  extremes.  . 

There  has  also  been  detected  a  small  annual  variation,  in  which 
the  needle  turns  its  north  pole  a  few  minutes  to  the  east  of  its 
mean  position  between  April  and  July,  and  to  the  west  the  rest 
of  the  year.  This  annual  oscillation  does  not  exceed  15  or  18 
minutes. 

619.  Diurnal  Variation. — The  needle  is  also  subject  to  a 
small  daily  oscillation.      In  the  morning  the  north  end  of  the 
needle  has  a  variation  to  the  east  of  its  mean  position  greater  than 
at  any  other  part  of  the  day.     During  winter  this  extreme  point 
is  attained  at  about  8  o'clock,  but  as  early  as  7  o'clock  in  the  sum- 
mer.    After  reaching  this  limit  it  gradually  moves  to  the  west, 
and  attains  its  extreme  position  about  3  o'clock  in  winter,  and 
1  o'clock  in  summer.     From  this  time  the  needle  again  returns 
eastward,  reaching  its  first  position  about  10  P.M.,  and  is  almost 
stationary  during  the  night.     The  whole  amount  of  the  diurnal 
variation  rarely  exceeds  12  minutes,  and  is  commonly  much  less 
than  that.     These  diurnal  changes  of  declination  are  connected 
with  changes  of  temperature,  being  much  greater  in  summer  than 
in  winter.     Thus,  in  England  the  mean  diurnal  variation  from 
May  to  October  is   10  or  12  minutes,   and   from  November  to 
April  only  5  or  6  minutes. 

620.  Magnetometer. — In   determining   and  observing   the 
variation   of    the   declination   use   is   made   of  a  magnetometer. 


OF  THE          lr 

MGfNIVE 

MAGNETOMETERS. 


3S9 


FIG.  342. 


Fig.  342  represents  such  an  instrument.  It  consists  of  a  mag- 
netized ring  surmounted  by  a  circular  mirror,  both  being  sus- 
pended by  a  silk  fibre.  The  poles  of  the 
ring  are  at  the  sides  and  the  plane  of 
the  ring,  when  at  rest,  coincides  with  the 
plane  of  the  magnetic  meridian.  Any  vari- 
ation of  the  meridian  is  followed  by  a  move- 
ment of  the  ring.  The  mirror,  being  con- 
nected with  the  ring,  moves  also.  This 
small  movement  may  be  magnified  and 
observed  by  means  of  a  telescope  and  scale. 
The  image  of  the  scale  is  reflected  from 
the  mirror  into  the  telescope. 

Surrounding  the  ring  magnet  is  a 
hollowed-out  piece  of  pure  copper.  This 
brings  the  magnet  quickly  to  rest  by  means 
of  the  electrical  currents  induced  in  it 
(Art.  671)  by  the  moving  magnet. 

Magnetometers  are  also  used  in  deter- 
mining the  magnetic  moment  of  bar  magnets. 

621.  Dip  of  the   Needle.— A  needle 

first   balanced   on  a  horizontal   axis,  and   then   magnetized   and 
placed  in  the  magnetic  meridian,  assumes  a  fixed  relation  to  the 

horizon,  one  pole  or  the 
other  being  usually  de- 
pressed below  it. 

The  axis  of  the  needle 
must  be  placed  very  ac- 
curately at  right  angles  to 
the  plane  of  the  magnetic 
meridian,  or  false  indications 
will  be  given ;  if  the  axis  of 
suspension  were  placed  in 
the  plane  of  the  meridian 
the  angle  of  depression 
would  be  90°  at  all  places 
on  the  earth's  surface. 

The  angle  of  depression  is 
called  the  dip  of  the  needle. 
Fig.  343  represents  the  dip- 
ping-needle, with  its  adjust- 
ing screws  and  spirit-level ; 
and  the  depression  may  be 
read  on  the  graduated  scale.  After  the  horizontal  circle  m  is 


FIG.  343. 


390  ELECTRICITY     AND     MAGNETISM. 

levelled  by  the  foot-screws,  the  frame  A  is  turned  horizontally  till 
the  vertical  circle  M  is  in  the  magnetic  meridian.  For  north 
latitudes,  the  north  end  of  the  needle  is  depressed,  as  a  in  the 
figure. 

622.  Isoclinic  Curves. — A  line  passing  through  all  points 
where  the  dip  of  the  needle  is  nothing,  i.e.,  where  the  dipping- 
needle  is  horizontal,  is  called  the  magnetic  equator  of  the  earth. 
It  can  be  traced  in  Fig.  344  as  an  irregular  curve  around  the 

FIG.  344. 


earth  in  the  region  of  the  equator,  nowhere  .departing  from  it 
more  than  about  15°.  At  every  place  north  of  the  magnetic 
equator  the  north-seeking  pole  of  the  needle  descends,  and  south 
of  it  the  south-seeking  pole  descends ;  and,  in  general,  the  greater 
the  distance,  the  greater  is  the  dip.  Imagine  now  a  system  of 
lines,  each  passing  through  all  the  points  of  equal  dip ;  these  will 
be  nearly  parallel  to  the  magnetic  equator,  which  may  be  regarded 
as  the  standard  among  them.  These  magnetic  parallels  are  called 
the  isoclinic  curves ;  they  somewhat  resemble  parallels  of  latitude, 
but  are  inclined  to  them,  conforming  to  the  oblique  position  of 
the  magnetic  equator.  In  the  figure,  the  broken  lines  show  the 
dip  of  the  south  pole  of  the  needle ;  the  others,  that  of  the  north 
pole.  The  points  of  greatest  dip,  or  dip  of  90°,  are  called  the 
poles  of  dip.  There  is  one  in  the  northern  hemisphere,  and  one  in 
the  southern.  The  north  pole  of  dip  was  found,  by  Captain  James 
C  Ross,  in  1831,  to  be  at  or  very  near  the  point,  70°  14'  N. ;  96° 
40'  W.,  marked  x  in  the  figure.  The  south  pole  is  not  yet  so  well 
determined. 

At  the  poles  of  dip  the  horizontal  needle  loses  all  its  directive 
power,  because  the  earth's  magnetism  tends  to  place  it  in  a  verti- 
cal line,  and,  therefore,  no  component  of  the  force  can  operate  in 


HORIZONTAL     INTENSITY.  391 

a  horizontal  plane.  The  isogonic  lines  in  general  converge  to  the 
two  dip-poles ;  but,  for  the  reason  just  given,  they  cannot  be 
traced  quite  to  them. 

The  dip  of  the  needle,  like  the  declination,  undergoes  a  varia- 
tion, though  by  no  means  to  so  great  an  extent. 

In  1576,  the  date  of  its  discovery,  the  dip  at  London  was 
71°  50';  it  increased  to  a  maximum  of  74°  42'  in  1723,  since 
which  time  it  has  gradually  decreased.  In  1879  the  dip  at  Kew 
was  67°  42'. 

In  the  course  of  250  years,  it  has  diminished  about  five  degrees 
in  London.  In  1820  it  was  about  70°,  and  diminishes  from  two 
to  three  minutes  annually. 

Since  the  dip  at  a  given  place  is  changing,  it  cannot  be  sup- 
posed that  the  poles  are  fixed  points  ;  they,  and  with  them  the  entire 
system  of  isoclinic  curves,  must  be  slowly  shifting  their  locality. 

623.  Intensity  of  the  Earth's  Magnetism. — The  axis  of 
the  dip-needle,  when  placed  in  the  magnetic  meridian,  coincides 
in  direction  with  the  lines  of  force  of  the  earth's  magnetic  field. 
The  magnetic  force,  then,  acts  in  this  inclined  direction.     In  most 
magnetic  determinations,  however,  the  needle  employed  swings  in 
a  horizontal  plane,  and  the  force  exerted  upon  it  by  the  earth  is 
only  that   portion   of   its   total   force   which   acts 
in   a  horizontal   direction.     This   horizontal   com-          FlG-  345> 
ponent  of  the  strength  of  the  field  is  called  the          ~fa 
horizontal  intensity  of  the  earth's  magnetism.     Let 
/  (Fig.  345)  represent  the  strength  of  the  earth's 

field    along    the    lines    of    force,    i.e.,    along    the     I 

axis   of   the    dip-needle,    d  =  angle    of   dip,    then 

h  —  the  horizontal  intensity.     From  the  diagram  it  is  seen  that 

h  =  I  cos  d. 

The  determination  of  the  horizontal  intensity  is  effected  after 
the  manner  described  in  Art.  608.  Its  values  for  places  in  North 
America  are  given  in  the  following  table  : 

HORIZONTAL  INTENSITY.    (C.  G.  S.  UNITS.) 

Boston 0.172 

Cleveland 0.184 

Chicago 0.184 

Halifax 0. 1 59 

Montreal 0.147 

New  York 0.184 

New  Orleans 0.281 

Niagara 0.167 

Philadelphia '. 0. 194 

San  Francisco 0.255 

Washington 0.200 


392  ELECTRICITY     AND     MAGNETISM. 

624.  Isodynamic  Curves. — An  inspection  of  the  table  just 
given  shows  that  the  horizontal  intensity  increases  as  we  near  the 
equator.  The  strength  of  the  earth's  field  in  the  direction  of  its 
lines  'of  force,  however,  decreases  on  nearing  the  equator,  as  might 
be  expected,  the  equator  being  farthest  from  the  poles.  After 
ascertaining,  by  actual  observation,  the  intensity  of  the  magnetic 
force  in  different  parts  of  the  earth,  lines  are  supposed  to  be  drawn 
through  all  those  points  in  which  the  force  is  the  same ;  these 
lines  are  called  isodynamic  curves,  represented  in  Fig.  346.  These 

FIG.  346. 


also  slightly  resemble  parallels  of  latitude,  but  are  more  irregular 
than  the  isoclinic  lines.  There  is  no  one  standard  equator  of 
minimum  intensity,  but  there  are  two  very  irregular  lines  sur- 
rounding the  earth  in  the  equatorial  region,  in  some  places  almost 
meeting  each  other,  and  in  others  spreading  apart  more  than  two 
thousand  miles,  on  which  the  magnetic  intensity  is  the  same. 
These  two  are  taken  as  the  standard  of  comparison,  because  they 
are  the  lowest  which  extend  entirely  round  the  globe.  The  inten- 
sity on  them  is  therefore  called  unity,  marked  1  in  the  figure.  In 
the  wide  parts  of  the  belt  which  they  include — lying  one  in  the 
southern  Atlantic,  and  the  other  in  the  northern  Pacific  oceans — 
there  are  lines  of  lower  intensity  which  return  into  themselves, 
without  encompassing  the  earth.  In  approaching  the  polar  regions, 
both  north  and  south,  the  curves,  retaining  somewhat  the  form  of 
the  unit  lines,  are  indented  like  an  hour-glass,  as  those  marked  1.7 
in  the  figure,  and  at  length  the  indentations  meet,  forming  an 
irregular  figure  8 ;  and  at  still  higher  latitudes,  are  separated  into 
two  systems,  closing  up  around  two  poles  of  maximum  intensity. 
Thus  there  are  on  the  earth  four  poles  of  maximum  intensity,  two 
in  the  northern  hemisphere  and  two  in  the  southern.  The  Ameri- 


ASTATIC    NEEDLES.  393 

can  north  pole  of  intensity  is  situated  on  the  north  shore  of  Lake 
Superior.  The  one  on  the  eastern  continent  is  in  northern  Siberia. 
The  ratio  of  the  least  to  the  greatest  intensity  on  the  earth  is 
about  as  0.7  to  1.9 ;  that  is,  as  1  to  2-|.  In  the  figure,  intensities 
less  than  1  are  marked  by  dotted  lines. 

625.  Variation  in  the  Strength  of  the  Earth's  Field.— 
Astatic  Needles. — The  intensity  of  the  earth's  magnetism  i& 
constantly  changing.  These  changes  consist  in  small  fluctuations 
about  an  average  constant  strength.  Many  electrical  determina- 
tions require  for  their  accuracy  either  that  the  horizontal  intensity 
should  remain  constant  01  that  its  fluctuations  should  be  taken 
into  account.  As  the  latter  is  the  only  alternative,  a  means  must 
be  had  of  determining,  at  any  moment,  whether  the  intensity  has 
changed,  and,  if  so,  how  much. 

One  method  is  to  employ  a  magnetometer  (Fig.  342),  which  is 
rendered  nearly  astatic  by  a  supplementary  bar  magnet.  (A  needle 
is  astatic  when  the  earth  has  no  directive  effect  upon  it.)  This 
auxiliary  magnet  is  placed  north  and  south,  directly  under,  or 
over,  the  needle  of  the  magnetometer.  When  placed  at  a  proper 
distance  above  the  needle,  depending  upon  its  strength,  it  will  act 
upon  the  needle  with  the  same  force  as  the  earth,  onl}'  in  an  op- 
posite direction.  It  will  thus  neutralize  the  influence  of  the  earth 
and  the  needle  can  turn  into  any  position.  If  the  magnet  be 
brought  a  little  nearer,  the  needle  will  suddenly  turn  around  and 
its  north-seeking  pole  will  point  south.  Now,  by  a  little  delicate 
manipulation,  the  needle  may  be  made  to  point  nearly  east  and 
west.  In  this  position  it  is  very  sensitive.  Any  small  increase  in 
the  earth's  intensity  will  cause  its  north-seeking  end  to  turn  to  the 
north,  and  any  decrease  to  the  south.  Thus,  by  looking  through 
the  telescope  at  the  mirror,  any  change  in 
the  intensity  can  be  detected  at  any  mo-  FIG.  347. 

ment,  and  the  amount  of  change  can  be 
arrived  at  by  calculation. 

Astatic  needles  are  of  great  value  in 
electrical  measurements.  Liberated  from 
the  earth's  directive  action  they  may  still 
be  affected  by  electrical  currents.  Another 
method  of  obtaining  this  end  is  shown  in 
Fig.  347. 

A  compound  needle,  consisting  of  two 
simple  needles  fixed  upon  a  wire,  with 

their  unlike  poles  opposed,  may  be  suspended  in  any  of  the  usual 
modes.  If  the  needles  are  exactly  equal  in  all  respects  the  system 


394  ELECTRICITY     AND     MAGNETISM. 

will  be  perfectly  astatic.     The  condition  of  perfect  equality  in  all 
the  conditions  is  never  realized. 

626.  Magnetic  Charts. — These  are  maps  of  a  country,  or  of 
the  world,  on  which  are  laid  down  the  systems  of  curves  which 
have  been  described.     But  for  the  use  of  the  navigator,  only  the 
isogonic  lines,  or  lines  of  equal  declination,  are  essential.     There 
are  large  portions  of  the  globe  which  have  as  yet  been  too  imper- 
fectly examined  for  the  several  systems  of  curves  to  be  accurately 
mapped.     It  must  be  remembered,  too,  that  the  earth  is  slowly 
but  constantly  undergoing  magnetic  changes,  by  which,  at  any 
given  place,  the  declination,  dip,  and  intensity  are  all  essentially 
altered  after  the  lapse  of  years.     A  chart,  therefore,  which  would 
be  accurate  for  the  middle  of  the  nineteenth  century,  will  be,  to 
some  extent,  incorrect  at  its  close. 

627.  The    Declination    Compass.— This   instrument  con- 
sists of  a  magnetic  needle  suspended  in  the  centre  of  a  cylindrical 
brass  box  covered  with  glass ;  on  the  bottom  of  the  box  within  is 
fastened  a  circular  card,  divided  into  degrees  and  minutes,  from 
0°  to  90°  on  the  several  quadrants.     On  the  top  of  the  box  are  two 
uprights,  either  for  holding  sight-lines  or  for  supporting  a  small 
telescope,  by  which  directions  are  fixed.     The  quadrants  on  the 
card  in  the  box  are  graduated  from  that  diameter  which  is  verti- 
cally beneath  the  line  of  sight. 

When  the  axis  of  vision  is  directed  along  a  given  line,  the 
needle  shows  how  many  degrees  that  line  is  inclined  to  the  mag- 
netic meridian.  In  order  that  the  angle  between  the  line  and  the 
geographical  meridian  may  be  found,  the  declination  of  the  needle 
for  the  place  must  be  known. 

628.  The  Mariner's  Compass. — In  the  mariner's  compass 
,{Fig.  348)  the  card  is  made  as  light  as  possible,  and  attached  to 

the  needle,  so  that  the  north  and 
south  points  marked  on  the  card 
always  coincide  with  the  magnetic 
meridian.  The  index,  by  which 
the  direction  of  the  ship  is  read, 
consists  of  a  pair  of  vertical  lines, 
diametrically  opposite  to  each 
other,  on  the  interior  of  the  box, 
These  lines,  one  of  which  is  seen 
at  a,  are  in  the  plane  of  the  ship's 
keel.  Hence,  the  degree  of  the  card  which  is  against  either  of 
the  lines  shows  at  once  both  the  angle  with  the  magnetic  meridian 
.and  the  quadrant  in  which  that  angle  lies. 


( 

AURORA    BOREALIS.  395 

In  order  that  the  top  of  the  box  may  always  be  in  a  horizontal 
position,  and  the  needle  as  free  as  possible  from  agitation  by  the 
rolling  of  the  ship,  the  box,  B,  is  suspended  in  gimbals.  The 
pivots,  A,  A,  on  opposite  sides  of  the  box,  are  centred  in  the  brass 
ring,  C,  D,  while  this  ring  rests  on  an  axis,  which  has  its  bear- 
in^s  in  the  supports,  E,  E.  These  two  axes  are  at  right  angles  to 
each  o'lier,  and  intersect  at  the  point  where  the  needle  rests  on  its 
pivot.  Therefore,  whatever  position  the  supports,  E.  E,  may  have, 
the  box,  having  its  principal  weight  in  the  lower  part,  maintains 
its  upright  position,  and  the  centre  of  the  needle  is  not  moved  by 
the  revolutions  on  the  two  axes. 

On  account  of  the  dip,  which  increases  with  the  distance  from 
the  equator,  and  is  reversed  by  going  from  one  hemisphere  to  the 
other,  the  needle  needs  to  be  loaded  by  a  small  adjustable  weight, 
if  it  is  to  be  used  in  extensive  voyages  to  the  north  or  south. 

629.  Aurora  Borealis. — This  phenomenon  is  usually  accom- 
panied by  a  disturbance  of  the  needle,  thus  affording  visible  indi- 
cations of  a  magnetic  storm;   but  the  contrary  is  by  no  means 
generally  true,  that  a  magnetic  storm  is  accompanied  by  auroral 
light.     The  connection  of  the  aurora  borealis  with  magnetism  is 
manifested  not  only  by  the  disturbance  of  the  needle,  but  also  by 
the  fact  that  the  streamers  are  parallel  to  the  dipping-needle,  as 
is  proved  by  their  apparent  convergence  to  that  point  of  the  sky 
to  which  the  dipping-needle  is  directed.     This  convergence  is  the 
effect  of  perspective,  the  lines  being  in  fact  straight  and  parallel. 

630.  Why  is  the   Earth  a  Magnet? — Modern  discoveries 
in  electro-magnetism  and  thermo-electricity  furnish  a  clew  to  the 
hypothesis  which  generally  prevails  at  this  day.     Attention  has 
been  drawn  to  the  remarkable  agreement  between  the  isothermal 
and  the  isomagnetic  lines  of  the  globe.     The  former  descend  in 
crossing  the  Atlantic  Ocean  toward  America,  and  there  are  two 
poles  of  maximum  cold  in  the  northern  hemisphere.     The  isoclinic 
and  the  isodynamic  curves  also  descend  to  lower  latitudes  in  cross- 
ing the  Atlantic  westward  ;  so  that,  at  a  given  latitude,  the  degree 
of  cold,  the  magnetic  dip,  and  the  magnetic  intensity,  are  each  con- 
siderably greater  on  the  American  than  on  the  European  coast. 
This  is  only  an  instance  of  the  general  correspondence  between 
these  different  systems  of  curves.     It  has  likewise  been  noticed 
(Art.  619)  that  the  needle  has  a  movement  diurnally,  varying  west- 
ward during  the  middle  of  the  day,  and  eastward  at  evening,  and 
that  this  oscillation  is  generally  much  greater  in  the  hot  season 
than  the  cold.     It  is  obvious,  therefore,  that  the  development  of 
magnetism  in  the  earth  is  intimately  connected  with  the  tempera- 


39G  ELECTRICITY    AND    MAGNETISM. 

ture  of  its  surface.  Hence  it  has  been  supposed  that  the  heat, 
received  from  the  sun  excites  electric  currents  in  the  materials  of 
the  earth's  surface,  and  these  give  rise  to  the  magnetic  phenomena. 
Most  interesting  is  the  hypothesis  recently  projected  by  Pro- 
fessor Bigelow,  viz.,  the  earth  is  revolving  and  moving  in  a 
magnetic  field,  which  is  created  by  the  sun.  According  to  this 
the  earth  is  a  magnet  by  induction  and  the  variations  in  its  mag- 
netism are  caused  by  differences  in  the  strength  of  the  field 
through  which  it  is  moving. 


CHAPTEK    V. 

CURRENT    ELECTRICITY. 

631.  Electricity  in  Motion.— It  has  been   seen  (Art.  571) 
that  when  conductors  which  have  a  difference  of  electrical  poten- 
tial are  connected  together  by  a  conducting  substance,  a  flow,  or 
current,  of  electricity  from  the  higher  to  lower  potential    takes 
place.     This  current,  however,  lasts  for  an  instant  only,  and  any 
phenomena  due  directly  to  the  flow  would  have  to  be  observed 
during  that  instant.     If  by  any  means  the  difference  of  potential 
of  the  bodies  could  be  maintained  in  spite  of  their  being  con- 
nected, a  continuous  current  would  be  made  to  traverse  the  con- 
necting conductor.      Such  a  means  was  accidentally  discovered  in 
1786,  by  Galvani,  Professor  of  Anatomy  at  Bologna.     After  exper- 
imenting, one  day,  upon  the  effects  of  statical  electricity  on  a 
frog's  leg,  he  hung  the  moist  leg,  by  means  of  a  copper  hook,  upon 
an  iron  window-guard.     He  then  noticed  that,  whenever  the  free 
end  of  the  leg  touched  the  guard,  it  gave  a  spasmodic  twitch,   as 
though  a  statical  charge  had  been  passed  through  it.     He  accord- 
ingly surmised  that  he  had  found  a  new  method  of  obtaining 
electricity. 

632.  Galvanic    Cells.  —  Galvani's  discovery   has  developed 
into  the   Galvanic  Cell  or  Element — an  arrangement  of  apparatus 
designed  to  give  a  continuous  flow  of  electricity. 

If,  when  two  different  substances  are  submerged  in  an  oxidizing 
fluid,*  one  of  them  has  a  greater  affinity  for  oxygen  than  the  other, 
then  a  difference  of  potential  will  be  set  up  between  them.  The 
one  having  the  greater  affinity  will  have  a  lower  potential.  If  de- 
sirable, the  substances  may  be  considered  as  having  become  elec- 
trified— the  least  oxidizable  positively,  and  the  other  negatively. 

*  For  simplicity,  affinity  for  oxygen  is  alone  mentioned  here.  The  princi- 
ple is  true  for  any  chemical  affinity. 


ELECTROMOTIVE     FORCE.  397 

If,  now,  the  substances  be  connected  by  a  wire,  a  current  will 
flow  through  it  from  the  higher  to  the  lower  potential.  As  long  as 
the  chemical  action  keeps  up,  the  difference  of  potential  and  the 
current  resulting  from  it  will  be  maintained. 

If,  for  example,  the  two  substances  were  copper  and  zinc 
plates,  and  the  fluid  was  dilute  sulphuric 
acid  (Fig.  349),  the  zinc,  having  greater 
affinity  for  the  oxygen  of  the  acid,  would 
have  a  lower  potential  than  the  cop- 
per. Upon  connecting  them  by  a  wire,  a 
current  would  flow  from  the  copper  to  the 
zinc.  This  would  be  a  simple  galvanic  ele- 
ment. 

The  arrangement  need  not  be  as  shown 
in  the  figure,  for  a  zinc  rod,  wrapped  in 
blotting-paper,  upon  which  is  wound  bare 
copper  wire,  would,  upon  moistening  the  paper  with  dilute  acid, 
give  a  current. 

The  flow  from  copper  to  zinc,  in  the  connecting  wire,  is  always 
accompanied  by  an  equal  flow  from  zinc  to  copper  through  the 
submerging  fluid.  (This  latter  flow  is  found  necessary  for  the 
maintenance  of  the  potential  difference.)  -  Thus,  if  we  start  at  any 
point  and  follow  the  current,  we  will  eventually  come  back  to  the 
point  whence  we  started,  i.e.,  a  current  of  electricity  always  flows  in 
a  closed  circuit. 

633.  Electromotive  Force. — The  difference  of  potential  set 
up  in  a  galvanic  element  is  due  to  an  Electromotive  Force,  which 
is  generally  represented  by  the  letters  E.  M.  F.  Its  amount  de- 
pends upon  the  nature  of  the  two  substances  employed — their 
relative  affinities  for  the  active  part  of  the  fluid.  In  dilute  sul- 
phuric acid  they  arrange  themselves  in  the  following  order : 

Hydrogen, 
;.i  Zinc, 

Iron, 

Lead, 

Nickel, 

Bismuth, 

Copper, 

Carbon, 

Silver, 

Platinum, 

Oxygen. 

Of  the  metals  given,  zinc  has  the  greatest  affinity  for  oxygen, 
and  platinum  the  least.  These  two  metals  then  would  give  the 


39S  ELECTRICITY     AND     MAGNETISM. 

greatest  E.  M.  F.  Platinum  and  silver  would  give  hardly  any.  If 
two  elements  be  constructed,  using  lead-zinc  for  one  and  lead-cop- 
per for  the  other,  the  current  would  flow  out  of  the  lead  in  the 
first  case,  and  into  the  lead  in  the  second. 

The  absolute  electrostatic  unit  of  potential  difference  is  too 
large  for  practical  purposes,  hence  a  practical  unit  of  E.  M.  F., 
called  the  -volt  (=  ^J¥  electrostatic  unit)  is  employed.  The  E.  M. 
F.  of  copper-zinc  in  dilute  sulphuric  acid,  at  the  instant  of  making 
first  contact,  is  0.921  volt. 

The  E.  M.  F.  of  a  cell  is  independent  of  the  size  of  the  electrodes. 

A  copper-zinc  cell  of  1  sq.  cm.  electrodes  has  the  same  E.  M. 
F.  as  one  with  1,000  sq.  cms. 

The  total  E.  M.  F.  in  a  circuit  is  equal  to  the  algebraic  sum  of 
the  separate  E.  M.  F.  'a. 

Thus,  if  two  copper-zinc  cells  be  connected  in  a  circuit  in  the 
order  (Cu— Zn)  — (Zn— Cu)  one  will  tend  to  send  a  current  in  one 
direction,  and  the  other  in  the  opposite  direction.  The  result  will 
be  no  current  at  all. 

If,  in  trying  this  experiment,  one  of  the  cells  be  very  large  and 
the  other  very  small,  the  fact  that  no  current  flows  would  illustrate 
the  fact  that  the  E.  M.  F.  is  independent  of  the  size  of  electrodes. 

634.  Polarization. — If  a  copper-zinc  sulphuric-acid  cell  be 
connected  with  an  electric  bell  (or  any  other  current  indicator)  it 
will  at- first  ring  loudly,  but  will  soon  weaken,  and  finally  cease  to 
give  a  sound.     Upon  investigating  the  cause  of  this  weakening  it 
will  be  found  that  the  E.  M.  F.  has  fallen  from  1  volt  to  possibly 
0.2  volt.     This  is  because  the  current,  which  the  element  has  sent 
through  its  own  liquid,  has  decomposed  that  liquid,  and  hydrogen 
(Art.  678)  has  been  deposited  upon  the  copper  and  oxygen  upon 
the  zinc.     The   oxygen   immediately   enters  into    chemical  union 
with  the  zinc,  but  the  hydrogen  remains  in  its  gaseous  form.     The 
hydrogen,  from  its  affinity  for  oxygen,  sets  up  a  counter  E..M.  F., 
tending  to  send  a  current  in  an  opposite  direction.     The  resulting 
•current  is  smaller  than  at  first,  and  the  cell  is  said  to  have  become 
polarized. 

635.  Types  of  Batteries. — (A  collection  of  galvanic  cells  is 
termed  a  battery.)     Practical  cells,  designed  for  giving  a  constant 
flow  of   electricity,    employ   different   methods   for   avoiding   the 
counter   E.  M.  F.  of   polarization.     The  market  affords  a  great 
variety,  but  we  need  consider  but  three  : 

BUNSEN'S  CELL. — As  has  been  shown,  the  counter  E.  M.  F.  is 
due  to  hydrogen  upon  the  electrode  having  the  higher  potential. 


BATTERIES. 


399 


FIG.  350. 


In  Bunsen's  cell  this  hydrogen  is  made  to  combine  with  oxygen 
furnished  by  nitric  acid.  The  cell  (Fig.  350)  employs  two 
different  acids,  which  are  kept  separate 
by  a  porous,  unglazed  cup.  This  allows 
the  electricity  to  flow,  but  prevents  a 
free  mixture  of  the  acids.  Outside  the 
cup  is  zinc  in  dilute  sulphuric  acid  ;  in- 
side is  carbon  in  nitric  acid.  The  hy- 
drogen, which  above  was  deposited  upon 
the  copper,  now  comes  off  at  the  carbon. 
Instead  of  being  allowed  to  exert  a  coun- 
ter E.  M.  F.,  it  is  immediately  oxidized 
l>y  the  nitric  acid.  On  the  other  hand, 
this  acid  is  prevented  by  the  porous  cup 
from  violently  attacking  the  zinc. 

This  cell  has  an  E.  M.  F.  of  1.8  volt, 
and  is  capable  of  maintaining  it  for  a 
long  time.  It  is  a  disagreeable  cell  to 
work  with  because  of  the  nitric-acid 
fumes.  These  fumes  can  be  avoided  by 
substituting  a  solution  of  bichromate  of 
potash  for  the  nitric  acid.  It  is  also  an  active  oxidizer  ;  but,  in 
time,  large  crystals  form  inside  the  walls  of  the  porous  cup  and 
cause  them  to  break  in  pieces. 

DANIELL'S  CELL. — This  cell  is  more  used  than  any  other,  in  the 
laboratory.  It  also  employs  two  liquids  and 
a  porous  cup.  The  arrangement  is  (Fig. 
351)  zinc  in  dilute  sulphuric  acid  inside  the 
cup,  and  copper  in  copper  sulphate  outside. 
The  cell's  own  current,  instead  of  depositing 
hydrogen  upon  the  copper,  deposits  copper 
from  its  sulphate.  Now  copper  upon  copper 
cannot  alter  the  E.  M.  F.  of  the  cell,  and 
hence  the  Daniell  has  the  most  constant  E.  M. 
F.  of  ordinary  cells.  The  E.  M.  F.  depends 
somewhat  upon  the  dilution  of  the  sul- 
phuric acid,  but  is  very  nearly  1  volt  for  any 
arrangement. 

A  modified  form  of  Daniell's  cell,  called  the  gravity  cell,  is  used 
in  telegraphy.  The  porous  cup  is  dispensed  with,  and  the  two 
liquids  are  kept  separate  by  the  action  of  gravity.  The  dilute  sul- 
phuric acid  is  floated  on  top  of  the  copper  sulphate. 

LECLANCHE  CELL. — There  are  more  of  this  form  of  cell  in  use 
than  of  all  others  put  together.  They  are  not  designed  to  main- 


FIG.  351. 


OF  THE 

TINTVE'RRTTV 


400 


ELECTRICITY    AND    MAGNETISM. 


FIG.  352. 


tain  a  constant  E.  M.  F.  for  any  great  length  of  time.     They  are- 
intended  for  purposes  where  a  current  is  needed  for  only  a  few 

moments  at  most,  as  for  electric 
bells  or  on  telephone  circuits.  After 
use  they  regain  their  original  E.  M. 
F.  The  arrangement  (Fig.  352)  is 
zinc  and  carbon  in  a  solution  of  sal 
ammoniac  (NH4C1).  An  attempt  is 
made  to  get  rid  of  the  hydrogen  of 
polarization  by  surrounding  or  mix- 
ing the  carbon  with  an  oxide  of 
manganese.  This  eventually  oxi- 
dizes the  hydrogen,  but  not  as 
rapidly  as  the  nitric  acid  in  Bun- 
sen's  cell.  Some  forms  of  Le- 
clanche  cell  employ  a  porous  cup 
containing  the  carbon  amid  the 
manganese  oxide.  The  E.  M.  F.  of 
a  fresh  Leclanche  is  1.5  volt. 


636.  Combustion  of  Zinc. — 
Nearly  all  batteries  employ  zincs  for 
the  lower  potential  electrode.  A 
current  flow  is  always  accompanied 

by  an  oxidation  of  zinc,  and  the  energy  which  accompanies  the 
current  comes  from  this  oxidation.  This  is  parallel  to  the  case  of 
a  steam-engine,  where  the  energy  comes  from  the  oxidation  of  the 
fuel  under  the  boiler. 


637.  Amalgamation  of  Zincs. — Ordinary  commercial  zinc  is 
impure.  If  this  impurity  were,  say  copper,  and  a  particle  should 
be  embedded  near  the  surface  of  a  zinc  electrode,  then,  upon  im- 
mersing in  acid,  the  zinc  and  copper  would  form  a  small  cell  by 
themselves.  This  would  be  giving  a  current,  whether  the  complete 
cell  were  in  use  or  not,  and  would  be  continually  wasting  zinc. 
This  wasting  of  zinc,  because  of  impurities  in  it,  is  called  local 
action  of  the  cell. 

It  has  been  found  that  local  action  can  be  prevented  by  amal- 
gamating the  zinc.  This  is  done  by  dipping  the  zinc  in  acid  and 
then  in  mercury.  The  mercury  unites  with  the  zinc  and  floats: 
the  impurities  to  its  surface.  These  are  then  detached  by  the  gas 
bubbles,  which  are  caused  by  their  union  with  the  acid.  The  zinc 
of  the  amalgam  is  oxidized  by  the  action  of  the  battery,  but  the 
mercury  remains  unaffected.  It  is,  therefore,  constantly  going 


RESISTANCE.  401 

Into  combination  with  new  zinc,  as  the  action  of  the  battery  con- 
tinues. 

638.  Practical  Units  of  Current  and  Quantity. — As,  in 
considering  the  flow  of  water  in  a  pipe,  we  give  the  current  a 
definite  value  of  say  so  many  gallons  per  hour,  so  we  can  give  a 
definite  value  to  the  electrical  current. 

The  quantity  of  water  passing  through  any  cross-section  of  a 
water-pipe  of  varying  diameter  is  the  same  for  the  same  time  and 
current.  Likewise 

The  quantity  of  electricity  passing  in  the  unit  time  through  any 
-cross-section  of  a  simple  undivided  circuit  is  the  same  for  the  same 
-current. 

To  obtain  a  unit  for  current  we  have  only  to  use  the  unit  for  quan- 
tity and  the  one  for  time.  Now,  the  absolute  electrostatic  unit  of 
quantity  is  not  of  convenient  size  for  practical  purposes.  Hence,  a 
new  unit,  termed  the  Coulomb,  is  employed.  It  equals  3,000,000,000 
absolute  electrostatic  units.  We  have,  then, 

The  practical  unit  of  current,  the  ampere,  is  that  current  which 
•delivers  one  coulomb  per  second  to  any  cross-section  of  the  circuit. 

639.  Resistance. — All  substance  offers  a  resistance  to  the  flow 
of  electricity.     Just  as  motion  against  resisting  friction  produces 
heat,  so  a  current  overcoming  electrical  resistance  produces  heat. 

The  resistance  offered  by  a  given  conductor  depends  upon  two 
things,  viz.,  the  character  of  the  substance  and  its  shape.  If  we 
represent  the  length  of  a  conductor  by  I  metres,  its  cross-section 
toy  q  sq.  mm.,  then  its  electrical  resistance 

—  T 

s  being  a  constant  depending  upon  the  character  of  the  substance 
and  termed  its  specific  resistance.*  If  we  assumed  s,  I,  and  q  each 
equal  to  unity,  we  would  have  a  unit  resistance.  A  unit,  much 
used  in  Germany,  the  Siemen's  quicksilver  unit,  is  defined  by  as- 
suming that  s  for  quicksilver  at  0°  C.  is  unity.  Hence,  Siemen's  unit 
of  resistance  is  the  resistance  offered  by  a  column  of  quicksilver  1  me- 
tre long  and  1  sq.  mm.  cross-section,  at  0°  C. 

The  international  practical  unit,  the  legal  ohm,  is  a  little  larger 
than  the  Siemen's  unit. 

1  ohm  —  1.06  Siemens  unit. 

If  R  represents  the  resistance  of  a  conductor,  J/*  evidently  repre- 
sents its  conductivity — the  greater  the  resistance  the  smaller  the 

*  The  absolute  specific  resistances  depending  upon  I  and  q  being  measured  in 
•centimetres,  and  Bin  absolute  units,  are  expressed  by  unwieldy  numbers,  and 
a  comprehension  of  the  subject  does  not  require  their  consideration. 


402  ELECTRICITY    AND    MAGNETISM. 

conducting  power.     Accordingly,  7s  can  be  called  the  specific  con- 
ductivity of  a  substance. 

SPECIFIC  CONDUCTIVITIES,  k  =  J/^ 

Mercury 1.06 

Silver 63. 

Copper 58. 

Iron 7.4  to  9.5 

Platinum 6.9 

German  silver 2.5  to  6.4 

Zn  SO4  (sat.  soU) 0000043 

Pure  Water 000000000025 

Glass 0 

These  figures  evidently  represent  the  length  in  metres  of  a 
•wire  of  1  sq.  mm.  cross-section,  that  the  resistance  may  be  1  ohm. 

Their  application  can  be  best  understood  by  an  example.  Deter- 
mine the  resistance  of  a  copper  wire  11.6  m.  long  and  0.1  sq.  mm. 
in  cross-section. 

7  1 1  A 

R  =  - —  =  •== — -7—  —  2  ohms. 
kq       58  x  0.1 

Silver  and  copper  are  the  best  conductors  we  have.  Because  of 
the  expense  of  the  former,  copper  is  universally  employed  on 
electrical  circuits.  In  fact,  some  modern  copper  is  said  to  con- 
duct better  than  silver.  Absolutely  pure  water  is  probably  a  non- 
conductor. The  purest  water  yet  obtained,  if  placed  in  a  tube 
of  unit  diameter  and  1  mm.  long  would  offer  the  same  resistance 
as  a  copper  wire  of  same  diameter,  but  as  long  as  the  orbit  of  the 
moon. 

The  influence  of  specific  conductivity  upon  resistance  can  be 
prettily  shown  by  the  following  experiment :  Pass  the  current 
from  a  dynamo  through  an  electric  lamp,  and,  by  means  of  two 
electrodes,  through  a  vessel  of  rain-water.  As  long  as  the  water  is 
pure  the  lamp  will  not  be  illuminated.  Place  a  few  drops  of  sul- 
phuric acid  in  the  water,  and  the  lamp  will  instantly  commence  to 
glow. 

640.  Influence  of  Temperature. — The  resistance  of  con- 
ductors changes  with  the  temperature.  In  all  metals  an  increase 
of  temperature  increases  the  resistance.  At  ordinary  temperatures 
the  increase  for  most  pure  metals  is  0.004  of  the  whole,  per  de- 
gree centigrade.  The  amount  for  German  silver  is  about  0.0003. 

Carbon  and  liquids  decrease  in  resistance  when  the  temperature 
is  raised.  The  change  per  degree  for  liquids  is  between  two  and 
three  per  cent. 

The  dependence  of  resistance  upon  temperature  furnishes  a 
means  of  measuring  the  latter.  A  conductor  of  large  temperature 


oiiri'3   LAW.  403 

coefficient  is  subjected  to  the  heat  whose  temperature  is  to  be  de- 
termined, and  while  still  in  place  its  resistance  is  measured.  The 
increase  of  resistance  furnishes  data  for  calculation  of  the  tempera- 
ture. By  this  means  Professor  Langley  has  measured  the  heat 
radiated  from  the  moon. 


641.  Ohm's    Law. — The  three  electrical   magnitudes — cur- 
rent, E.  M.  F.,  and  resistance — are  connected  together  by  an  impor- 
tant relation  called  Ohm's  law.     Letting  E  represent,  in  volts,  the 
algebraic  sum  of  all  the  E.  M.  F.'s  of  a  circuit,  R  the  sum  of  all 
the  resistances,  in  ohms  (of  battery,   conducting  wires,   and  all 
instruments  in  circuit),  then  this  law  states,  the  current  strength 
in  amperes, 

The  strength  of  the  current  varies  directly  as  the  E.  M.  F.,  and 
inversely  as  the  resistance. 

642.  Divided   Circuits. — Shunts.  —  If   a   current  from  a 
battery   of   E.  M.  F.   —  E  and   internal  resistance  —  r  be  sent 
through  a  wire  which  divides  at  a  certain  point  (Fig.  353)  into 
two   branches,   which   however   re- 
unite further  on,  and  if  the  resist- 
ances of  the  undivided  conductor 

and  its  branches  are  E,  rlt  ra  re- 
spectively, then  the  substitution  of 
r  -+•  R  4-  r1  +  r,  in  Ohm's  law 
would  not  give  the  correct  current 
strength.  The  reason  for  this  is 
that  the  whole  current  does  not 
pass  through  each  of  the  branches 
rl  and  r2.  They  each  take  a  por- 
tion of  the  current,  depending  upon  their  resistances.  A  single 
conductor  might  be  found,  which,  if  substituted  for  the  two, 
would  leave  the  current  in  R  unchanged.  The  resistance  of  this 
single  conductor  might  be  called  the  equivalent  resistance  of  the 
branches.  To  determine  this  equivalent  resistance  it  is  most  con- 
venient to  consider  the  conductivities  of  the  branches.  Evidently 
the  conductivity  of  the  single  replacing  conductor  must  equal  the 
sum  of  the  conductivities  of  the '  separate  paths.  But  the  con- 
ductivities are  the  reciprocals  of  the  resistances.  Hence  we  have 


404:  ELECTRICITY     AND     MAGNETISM. 

The   current   C  flowing   through   the   undivided   portion   of  the 
circuit,  e.g,,  through  72,  would  be,  by  Ohm's  law, 
E          _ E_ 

R  +  r  +  K       E  +  r  +  ~^^- 

r,  +  r, 

In  the  same  manner  the  equivalent  resistance  of  any  number  of  dif- 
ferent paths  may  be  determined. 

When  a  conductor  is  placed  so  as  to  take  a  portion  of  the 
current  which  is  passing  through  another  conductor  it  is  called 
a  shunt  and  the  current  is  said  to  be  shunted. 

Many  delicate  instruments  for  measuring  electrical  quantities 
would  be  ruined  if  the  whole  current  passed  through  them.  In 
such  cases  a  portion  of  the  current  is  shunted  off  from  the  instru- 
ment. From  the  known  resistances  of  the  instrument  and  the 
shunt  the  quantities  to  be  determined  can  be  calculated. 

643.  Ratio  of  Currents  in  Shunts. — In  order  to  determine 
the  portion  of  the  current  flowing  in  any  branch  of  a  divided 
circuit,  we  must  consider  that  the  whole  current  is  carried  by 
the  branches  as  a  whole.     Letting  C  =  current  in  undivided  por- 
tion (Fig.  353)  and  cl  and  c2  =  currents  in  rl  and  ra,  we  have 

C  =  c,  +  c,. 

Again,  bearing  in  mind  that  the  difference  of  potential  (E.  M.  F.) 
between  the  ends  of  each  branch  is  the  same  —  e,  we  have,  by 
Ohm's  law, 

e  .  e 

c,  =-.«.  =  -.  "to. 

. '.  c.  :  a.  :  etc.  =  —  :  —  :  etc. 
r,       r2 

The  currents  carried  by  different  branches  between  two  points  of  a 
circuit  are  inversely  as  the  resistances  of  the  branches. 

644.  Fall  of  Potential. — If  we  have  a  battery  connected 
through  a  uniform  straight  wire  of  given  resistance,  we  may  con- 
sider the  potential  at  the  zinc  end  to  be  =  zero,  and  that  at  the 
other  end  positive,  and  =  E.  M.  F.  of  the  battery.     Now,  inasmuch 
as  the  resistances  of  equal  lengths  of  the  wire  are  the  same,  the 
potential  at  the  middle  of  the  wire  equals  one-half  the  E,  M.  F, 
At  one-quarter  the  distance  from  each  end  of  the  wire  the  poten- 
tials are  one-quarter  and   three-quarters   of   the  E.  M.  F.     The 
potential  varies  all  along  the  wire,  from  zero  at  the  zinc  end  to  E. 
M.  F.  at  the  other  end.     If  we  commence  at  the  other  end  we  may 
say  that 

The  potential  falls  directly  as  the  resistance. 

Of  course,  if  the  conductor  were  not  homogeneous,  e.g.,  made 


WHEATSTONE'S    BRIDGE. 


405 


FIG.  355. 


of  copper  and  then  German  silver,  the  fall  would  not  be  the  same 
for  the  same  lengths.     It  would  be  more  rapid  in  the  German 
silver   portion    of    the    circuit 
than  in  the  copper  portion.  FIG.  354. 

645.  Resistance    Boxes 
or     Rheostats. — These    are 
boxes  (Fig.  354)  containing  dif- 
ferent   spools    of    wire,    whose 
resistances    have    been    deter- 
mined, and  which  can  be  used 
for    standards    of    comparison. 
-German   silver  wire   is    gener- 
ally   used,   because    its    resist- 
ance   changes    least   with    the 
temperature.  The  proper  length 
of  wire  is  taken,  and,  after  be- 
ing doubled  at  its  middle  (Fig.  355),  is  wound  upon  a  spool,  the 
two  parts  being  wound  side  by  side.     This  is  indicated  in  the 

figure.  The  reason  for  this  doubling  is 
to  avoid  the  self-induction  disturbances 
of  the  wire  (Art.  668).  The  spool,  when 
wound,  is  placed  inside  the  box  and  the 
terminals  are  fastened  to  two  separate 
brass  blocks  on  the  top  of  the  box.  To 
each  of  these  blocks  is  fastened  one  end 
of  the  two  neighboring  coils.  In  the 
^4.  figure,  a  and  b  of  one  resistance  are 

fastened  to  blocks  E  and  H.     The  ends 

'C  and  d  of  the  neighboring  coil  are  fastened,  one  to  H  and  the 
other  to  M.  The  blocks  can  be  connected  together  at  will  by 
brass  plugs  fitting  into  holes  between  them. 

Suppose,  now,  that  the  two  terminals  of  a  battery  be  connected 
with  E  and  M  respectively.  If  the  plugs  1  and  2  be  removed,  the 
current  will  be  obliged  to  traverse  both  of  the  resistance  coils.  If 
plug  1  be  inserted,  the  current  will  divide  between  the  plug  and 
the  coil.  But  the  resistance  of  the  plug  is  infinitesimal,  and  hence, 
practically,  the  whole  current  passes  through  it  and  none  through 
the  coil. 

When  a  box  of  coils  is  inserted  in  a  circuit,  the  resistance  can 
be  varied  at  will,  by  simply  inserting-  or  pulling  out  plugs. 

646.  Wheatstone's  Bridge. — An  important  application  of 
the  preceding  principles  is  Wheatstone's  bridge.     It  is  an  arrange- 


406 


ELECTRICITY    AND     MAGNETISM. 


merit  of  apparatus  by  means  of  which  resistances  can  be  very  accu- 
rately determined. 

If  a  current  of  electricity  arriving  at  V  (Fig.  356)  divides  and 


by  two  paths,  A  B  and  CD,  to  V,  where  the  paths 
unite,  then  the  difference  of  potential  (V-V)  is  acting  on  both 
paths.  The  potential  along  each  path  must  fall  from  V  to  V.  If 
at  any  point  of  the  path  A  B,  the  potential  is  g,  then  some  point  (g'} 
of  the  other  path,  CD,  can  be  found  having  *  the  same  potential. 
If  these  two  points,  g  and  g'  be  connected  through  a  galvanometer 
or  any  other  current  detector,  no  current  will  flow,  because  there  is 
no  potential  difference  between  g  and  g'. 

Inasmuch  as  the  fall  or  loss  of  potential  along  each  path  is  pro- 
portional to  the  resistance,  the  loss  in  passing  A  must  be  the  same 
as  in  passing  C,  and  the  resistance  of  A  must  bear  the  same  ratio 
to  A  -f  B  as  C  does  to  C  +  D.  In  order  that  the  potentials  may  be 
the  same  at  g  and  g',  it  must  be  true  that  the  resistances  follow 

the  proportion 

A-.B  =  C:D. 

In  Wheatstone's  bridge,  when  no  current  passes  through  the 
galvanometer,  the  products  of  the  opposite  resistances  are  equal. 

The  method  of  determining  resistances  by  the  bridge  is  to  place 
the  unknown  resistance  in  one  arm  of  the  bridge,  as  D.  Known 
resistances  are  placed  in  A  and  B,  and  a  resistance-box  in  C.  By 
manipulating  the  plugs  in  C  a  balance  can  be  made  so  that  no  cur- 
rent flows  through  the  galvanometer.  A,  B,  and  C  are  known,  and 
the  required  resistance 


It  is  sometimes  convenient  to  make  G  constant,  and  vary  bo^h 
A  and  B  until  a  balance  is  obtained,  A  and  B  consisting  of  parts 
of  the  same  straight  wire  of  uniform  diameter.  The  balance  is 


ARRANGEMENT    OF    CELLS.  40T 

obtained  by  sliding  the  contact  (g)  with  the  galvanometer  along 
this  wire.  The  resistances  of  A  and  B  are  then  proportional  to 
their  lengths. 

647.  Cells  in  Series  and  in  Multiple  Arc.— A  battery  of 
two  cells  can  be  connected  to  a  circuit 
in  two   different  manners.     The  copper  FIG.  357. 

of  one  may  be  connected  to  the  zinc  of  1 1   1 1 

the   other   (Fig.    357),    and    the  circuit     <  \\\\ 

connected   to   the  remaining    zinc    and  !  I  ca 

copper.     The   cells  would    then    be  in 

series.  Again,  the  coppers  of  each  and  the  zincs  of  each  might 
be  connected  together  and  the  circuit  connected  to  these  short 

connecting  wires  (Fig.  358).     The  two 

cells  are  then  said  to  be  in  multiple  arc. 

Jl  Let   us   consider   the   results   of    these 

/||\  different  arrangements.     Represent  the 

<          (        j E.  M.  F.  of  each  cell  by  E,  and  the  in- 

\|L/  ternal  resistance  by  r. 

Evidently,  when  in  series,  the  E.  M. 
F.  of  the  circuit  is  equal  to  the  sum  of 

the  two  E's,  and  the  internal  resistance  of  the  battery  is  2  r.  If 
the  resistance  of  the  total  external  circuit  be  R,  then  the  current, 
when  the  cells  are  in  series, 

c--=  R  2+E2  r- 

When  the  cells  are  in  multiple  arc,  the  E.  M.  F.  is  no  greater 
than  for  a  single  cell.  The  two  cells  are  like  a  single  cell  of  twice 
the  size,  and  size  does  not  affect  the  E.  M.  F.  (Art.  633).  The  re- 
sistance, however,  is  only  half  that  of  a  single  cell,  because  the 
cross-section  of  the  liquid,  which  the  current  has  to  pass,  is  twice 
as  great.  For  two  cells  in  multiple  arc,  then,  the  current 


We  can  extend  this  reasoning  to  any  number  of  cells,  and  say, 
n  cells,  in  series,  multiply  the  E.  M.  F.  and  the  internal  resistance 

by  n,  and  m  cells,  in  multiple  arc,  divide  the  internal  resistance  by 

m,  but  leave  the  E.  M.  F.  unaltered,  it  being  that  of  a  single  cell. 

In  general,  if  we  have  m  n  cells,  consisting  of  n  groups  in  series. 

each  group  containing  m  cells  in  multiple  arc,  the  resulting  cur- 

rent will  be 


0= 


R  +  n  — 
m 


408  ELECTRICITY    AND    MAGNETISM. 

With  a  given  number  of  cells  and  a  given  external  resistance 
some  arrangement  of  the  cells  can  be  found  which  will  give  a  maxi- 
mum current.  It  can  be  proved  that  this  arrangement  will  ren- 
der the  internal  resistance  as  nearly  equal  to  the  external  as  possible. 

When  the  external  resistance  is  very  great  compared  with  the 
battery,  it  is  advisable  to  get  as  much  E.  M.  F.  as  possible.  This 
is  accomplished  by  placing  the  cells  in  series. 

Problems. 

1.  An  incandescent  lamp  takes  a  current  of  0.7  ampere,  and  the 
E.  M.  F.  between  its  terminals  is  found  to  be  98  volts  :  what  is  its 
resistance  ? 

2.  A  current  of  8.5  amperes  flows  through  a  conductor,  the 
ends  of  which  are  found  to  have  a  difference  of  potential  of  24 
volts  :  what  is  its  resistance?  Ans.  2.823  ohms. 

3.  A  battery,  arranged  in  series,  consists  of  5  Daniell  cells,  each 
having  an  E.  M.  F.  of  1.08  volt  and  an  internal  resistance  of  4 
ohms :  what  current  will  the  battery  produce  with  an  external  re- 
sistance of  7  ohms.  Ans.  0.2  ampere. 

4.  Two  cells  of  E.  M.  F.,  1.8  volt  and  1.08  volt  respectively, 
are  placed  in  circuit  in  opposition  (i.e.,  with  their  poles  in   such 
positions  that  the  cells  tend  to  send  currents  in  opposite  direc- 
tions).     The  current  is  found  to  be  0.4  ampere :   what  current 
will  be  produced,  if  the  cells  are  placed  properly  in  series? 

Ans.  1.6  ampere. 

5.  A  Bunsen  cell  has  an  internal  resistance  of  0.3  ohm  and 
its  E.  M.  F.  on  open  circuit  is  1.8  volt.     The  circuit  is  completed 
by  an  external  resistance  of  1.2  ohm  :  find  the  current  produced 
and  the  difference  of  potential  which  now  exists  between  the  ter- 
minals of  the  cell.  A        \  C  =  1.2  ampere. 

ns'  \P.D.  =  1.44  volt. 

6.  Two  wires  of  the  same  length  and  material  are  found  to  have 
resistances  of  4  and  9  ohms  respectively :  if  the  diameter  of  the 
first  is  1  mm.,  what  is  the  diameter  of  the  second? 

7.  The  resistance  of  a  bobbin  of  wire  is  measured  and  found 
to  be  68  ohms  :  a  portion  of  the  wire  2  metres  in  length  is  now  cut 
off,  and  its  resistance  is  found  to  be  0.75  ohm.     What  was  the 
total  length  of  wire  on  the  bobbin?  Ans.  181.3  metres. 

8.  What  length  of  platinum  wire  1  mm.  in  diameter  is  required 
in  order  to  make  a  10  ohm  resistance  coil? 

9.  A  wire  ra  metres  in  length  and  I/nth  of  a  millimetre  in  di- 
ameter is  found  to  have  a  resistance  r:  what  is  the  specific  re- 
sistance of  the  material  of  which  it  is  made  ? 


THE    CURRENT'S    LINES    OF    FORCE.  400 

10.  A  uniform  wire  is  bent  into  the  form  of  a  square  :  find  the 
resistance  between  two  opposite  corners  in  terms  of  the  resistance 
of  one  of  the  sides. 

11.  Twelve  incandescent  lamps  are  arranged  in.parallel  between 
two  electric  light  leads.     The  difference  of  potential  between  the 
leads  is  99  volts,  and  each  lamp  takes  a  current  of  0.75  ampere  : 
what  is  the  equivalent  resistance  between  the  leads  ? 

Ans.  11  ohms. 

12.  A  battery  of  20  ohms  resistance  is  joined  up  in  circuit  with 
a  galvanometer  of  10  ohms  resistance.     The  galvanometer  is  then 
shunted  by  a  wire  of  the  same  resistance  as  its  own  :  compare  the 
currents  produced  by  the  battery  in  the  two  cases. 

Ans.  C  :  G'  =  5  :  6. 

13.  In  the  preceding  example  determine  the  ratio  between  the 
currents  which  flow  through  the  galvanometer  before  and  after  it 
is  shunted. 

14.  How  would  you  arrange  a  battery  of  12  cells,  each  of  0.6 
ohm  internal  resistance,  so    as  to    send    the    strongest    current 
through  an  electro-magnet  of  resistance  of  0. 7  ohm. 

15.  In  a  Wheatstone's  bridge  (Fig.  356)  A  =  10  ohms,  B  = 
1,000  ohms,  and  C  =  50  ohms  :  what  is  the  resistance  of  D,  if  the 
galvanometer  shows  no  current?  Ans.  5,000  ohms. 


CHAPTEK   VI. 

ELECTRO -MAGNETISM. 

648.  The  Current's  Lines  of  Magnetic  Force. — If  a 
wire,  carrying  a  current  of  electricity,  be  passed  through  a  sheet  of 
paper,  as  indicated  in  Fig.  359,  and  if  iron  filings  be  sprinkled  upon 
the  paper,  they  will  arrange  themselves  so  as  to  form  circles  around 
the  wire.  If  then  a  short  magnetic  needle  be  moved  about  the 
wire,  it  will  tend  to  place  itself  tangentially  to  the  circle  passing 
through  its  centre.  If  the  direction  of  the  current  be  reversed, 
the  needle  will  turn  through  180°.  The  circles  of  the  filings  show 
the  paths  of  magnetic  lines  of  force,  which  owe  their  existence  to 
the  electrical  current,  just  as  the  filings  in  Fig.  335  showed  the 
paths  of  the  lines  of  force  of  a  magnet.  In  order  to  give  a  direc- 
tion to  these  circular  lines  we  must  consider  in  what  direction  an 
isolated  north  magnetic  pole  would  move.  In  the  diagram  this 


410 


ELECTRICITY    AND     MAGNETISM. 


would  evidently  be  contrary  to  the  motion  of  the  hands  of  a  clock. 
In  general,  to  remember  the  directions  which  these  lines  will  have, 


FIG.  359. 


BATTERY 


Maxwell  makes  use  of  the  thrust  and  turn  of  an  ordinary  screw 
(Fig.  360).     Suppose  the  current  to  flow  along  the  axis  of  the 

screw,   from   the   head 

FIG.  360.  to  the  point  when  it  is 

being  screwed  into  any- 
thing, and  vice  versa 
when  it  is  being  re- 
moved— i.e.,  the  direc- 
tion of  the  current  is  the  same  as  the  direction  of  propagation  of 
the  screw — then  the  direction  of  the  circular  lines  of  force  is  the 
same  as  the  motion  of  the  circumference  of  the  head  of  the  screw 
when  it  is  screwed  in  or  out. 


649.  Effect  of  a  Current  on  a  Magnet. —  The  experiment 
in  the  preceding  article  shows  that  there  is  a  connection  between 
electricity  and  magnetism.  In  1819,  Oerstedt  showed  that  a 
magnet  tends  to  set  itself  at  right  angles  to  a  wire  carrying 
an  electric  current.  He  found,  further,  that  the  way  in  which 
the  north  end  of  the  needle  turns,  whether  to  the  right  or  left  of 
its  normal  position,  depends  upon  the  position  of  the  wire  that 
carries  the  current — whether  it  is  above  or  below  the  needle— 
and  upon  the  direction  in  which  the  current  flows  through  the 
ivire.  The  position  which  a  magnet  will  tend  to  take,  when  under 


SOLENOIDS. 


411 


FIG.  361. 


the  influence  of  a  current,  can  be  easily  determined  by  knowing 
the  direction  of  the  lines  of  force  of  both  current  and  magnet, 
and  by  considering  that  the  magnet  will  move  in  such  a  direc- 
tion as  to  tend  to  bring  its  lines  of  force  into  the  same  path  and 
direction  as  the  lines  of  force  of  the  cur- 
rent. Sometimes  the  student  forgets  the 
direction  of  the  current's  lines.  In  such 
a  case  let  him  remember  that  if  the  cur- 
rent flows  from  South  to  North  and  Over 
the  needle,  the  north  end  of  the  needle 
will  be  turned  toward  the  West,  the  com- 
bination being  remembered  by  the  initial 
letters,  SNOW. 

If  we  suppose  the  magnet  to  be 
fixed,  and  the  conductor  carrying  the 
current  to  be  movable,  then  the  con- 
ductor will  move  because  of  the  strife 
toward  parallelism  of  their  lines  of  force. 
Lodge  illustrates  this  by  a  beautiful  ex- 
periment. Send  a  strong  current  through 
a  vertically  suspended  gold  thread  (such 
as  is  used  upon  military  garments). 
Alongside  the  thread  place,  vertically,  an 
electro-magnet  (Fig.  361).  Upon  excit- 
ing the  magnet  the  thread  will  wind  itself 
around  the  magnet.  Reverse  the  cur- 
rent and  it  will  unwind  and  then  rewind 
itself  in  the  opposite  direction.  Com- 
plete parallelism  of  the  lines  of  force  is,  of  course,  impossible, 
F  ogo  but  the  experiment  well  illustrates 

the  tendency. 

The  movement  of  a  needle  under 
the  influence  of  a  current  furnishes 
a  convenient  means  of  determining 
the  direction  in  which  the  current 
is  flowing. 

650.  Solenoids.  —  If  a  wire 
which  carries  a  current  be  bent  in- 
to a  circle,  all  the  lines  of  force  will 
emerge  from  one  side  of  an  imag- 
inary disc  bounded  by  the  loop 
(Fig.  362)  and  bending  around  the 
wire  will  enter  the  opposite  side. 
The  loop,  because  of  the  current,  will  be  magnetically  equivalent 


412 


ELECTRICITY     AND    MAGNETISM. 


FIG.  363. 


to  a  disc  magnet  having  north  polarity  on  one  side  and  south, 
polarity  on  the  other.     In   the   diagram  an  isolated  north  pole 

placed  above  the  surface  of  the 
page  would  be  attracted  to- 
ward £>,  as  though  it  were  a 
south  magnetic  pole.  If  the 
wire  is  coiled  into  the  shape 
indicated  in  Fig.  363,  it  is 
termed  a  solenoid  or  helix. 
Upon  passing  a  current,  the 
lines  of  force,  from  their  mut- 
ual action,  take  the  paths  indicated  in  the  figure.  A  solenoid, 
when  traversed  by  a  current,  has 
the  same  magnetic  effect  as  a  bar 
magnet  whose  axis  coincides  with 
the  axis  of  the  solenoid.  Sole- 
noids exhibit  all  the  properties 
of  magnets — attract  pieces  of  soft 
iron,  attract  and  repel  magnets 
or  other  solenoids,  and,  if  sus- 
pended by  non-restraining  quick- 
silver contacts,  as  in  Fig.  364,  will  turn  into  the  earth's  magnetic 
meridian. 


FIG.  364. 


FIG.  365. 


651.  Ampere's  Theory  of  Magnetism.— Because  of  the 

like  actions  exerted  by  sole- 
noids and  magnets,  Ampere 
concluded  that  the  perma- 
nent magnetism  of  steel 
owed  itself  to  circular  mole- 
cular currents  of  electricity, 
as  shown  in  Fig.  365.  He 
showed  that  the  resultant 
of  these  many  molecular 
currents  was  equivalent  to 
surface  solenoidal  currents, 
as  indicated  in  Fig.  366.  In  the  interior  of  the  magnet  cur- 
rents on  contiguous  molecules  are  running  in  opposite  directions, 
and  accordingly  neu- 
tralize each  other's  FIG.  366. 
magnetic  effects.  Half 
of  the  currents  on  the 
surface  molecules  are 
not  neutralized,  and  the  combined  effect  is  the  same  as  a  surface 
solenoidal  current. 


MAGNETO-MOTIVE    FORCE. 


413 


FIG    367. 


It  should  be  remembered  that  looking  at  the  north  end  of 
a  magnet,  end  on,  the  amperian  currents  run  counter-clockwise. 

652.  Electro-magnets. — We  have  seen  (Art.  611)  that  when 
a  piece  of  iron  is  placed  in  a  magnetic  field,  it  becomes  an  induced 
magnet  and  it  adds  lines  of  force  to  the  field.     Now,  if  an  iron 
core  be  inserted  into  a  solenoid,  it  becomes  a  magnet  under  the 
influence  of  the  solenoid's  field,  and,  because  of  its  much  greater 
permeability  than  air  (Art.  612),  adds  many  lines  of  force  to  the 
field.     Such  a  combination  is  termed  an  electro-magnet.     An  electro- 
magnet differs  from  an  ordinary  one  in  that  the  instant  the  excit- 
ing current  is  removed  the  electro-magnet  loses  its  magnetism. 

The  intensity  of  the  field  which  a  given  solenoid  can  produce  is 
limited  only  by  the  strength  of  the  current  traversing  it.  If  the 
current  strength  is  doubled,  the  strength  of  the  field  is  doubled. 
The  iron  core,  upon  being  inserted,  multiplies  the  strength  of  the 
field  by  a  certain  factor  (the  permeability  of  the  core,  see  Art. 
612).  Now,  if  the  permeability  of  iron  were  constant,  there  would 
be  scarcely  any  limit  to  the  strength 
which  could  be  given  to  an  electro- 
magnet. But  as  the  iron  reaches  the 
point  of  saturation  its  permeability 
decreases  toward  unity.  As  it  is, 
electro  magnets  can  be  made  many 
times  more  powerful  than  permanent 
magnets. 

A  common  form  of  electro-mag- 
net is  schematically  shown  in  Fig. 
367.  The  solenoid  with  its  core  is 
bent  into  the  form  of  a  horseshoe. 
An  actual  magnet  would  be  wound 
with  many  more  turns  of  wire,  which  must,  of  course,  be  insulated 
from  the  core.  Upon  passing  a  current,  a  heavy  weight  can  be 
suspended,  and  this  will  detach  itself  as  soon  as  the  current  is  dis- 
continued. 

653.  Magneto-motive  Force. — In  the  practical  construction 
of  electro-magnetic  apparatus  it   is  often   desirable  to  obtain  a 
maximum  number  of  lines  of  force  in  a  given  region.     This  region 
is  to  be  occupied  by  some  movable  armature  or  object,  to  be  sub- 
jected to  the  field's  influences.     Let  us  consider  how  this  can  be 
obtained  when  this  region  is  the  space  between  the  poles  of  an 
electro-magnet.     Evidently  by  increasing  the  number  of  lines  gen- 
erated by  the  current  and  adding  as  many  lines  as  possible  to  these 
by  proper  selection  of  materials  and  shape  of  the  electro-magnet. 


414  ELECTRICITY    AND     MAGNETISM. 

The  number  of  lines  originally  produced  will  increase  with  the 
current  strength  which  flows  through  the  solenoid  or  coil.  It 
will  also  increase  with  the  number  of  the  loops  of  the  wire  in  the 
coil  —  for  each  loop  will  add  the  same  number  of  lines  to  those 
already  traversing  the  axis  of  the  coil.  Accordingly  we  must 
employ  as  strong  a  current  and  as  many  turns  of  wire  as  pos- 
sible. Eemembering  that  the  magnetic  permeability  of  a  sub- 
stance is  the  same  as  its  conductivity  toward  lines  of  force,  it  is 
desirable  that  all  the  space  which  is  traversed  by  lines  of  force, 
except  the  portion  which  is  to  be  employed  for  the  movement 
of  the  object  to  be  subjected  to  the  field's  influence,  should  be 
occupied  by  a  substance  of  maximum  magnetic  permeability,  i.e., 
by  the  best  soft  iron. 

Now  we  can  obtain  a  law  for  the  flow  of  lines  of  magnetic  force 
exactly  like  Ohm's  law  (Art.  641)  for  current  flow.  Call  the  source 
of  the  lines  the  magneto-motive  force  (M.  M.  F.)  ;  call  the  reciprocal 
of  the  conductivity  the  magnetic  resistance  (E)  ;  then  the  magnetic 
flux  or  number  of  lines  which  pass  through  the  axis  of  the  coil 

M.  M.  F. 

*=—  R— 

Evidently  the  M.  M.  F.  is  a  function  of  the  current  strength  (c) 
and  the  number  of  loops  (n)  made  by  the  coil  wire.  It  can  be  shown 
mathematically  that  if.  c  is  expressed  in  amperes,  and  N  is  to  be 

obtained  in  absolute  units,  the  M.  M.  F.  =  —  -  n  c.     The  magnetic 

resistance  is  subject  to  the  same  law  as  electrical  resistance  (Art. 
639).  Increase  the  length  /  of  the  path  to  be  travelled  by  the 
lines  and  the  resistance  is  increased.  It  is  decreased  by  increas- 
ing the  cross-section  q,  and  decreases  with  increase  of  magnetic 
permeability  /A,  so  that  the  resistance 

E  =  -l- 

/x  q 

Introducing  these  values  in  the  equation  for  the  flux,  we  obtain 


10  — 
M 

This  formula  is  of  great  importance  and  has  been  of  great  service 
in  the  designing  of  efficient  electro-magnetic  machinery,  e.g.,  dy- 
namos and  motors.  To  understand  the  application  of  it,  let  us 
refer  to  Fig.  367.  The  region  where  maximum  flux  is  desired  is 
the  bottom  of  the  horseshoe  where  the  armature  and  the  weight 
attached  to  it  are  suspended.  The  flux  will  be  increased  by 
increasing  the  current  (c),  the  number  of  turns  of  wire  (n),  the  cross- 
sections  (q)  of  the  core,  the  armature  and  the  air  gaps  between  tLe 


THE    TELEGRAPH.  415 

armature  and  the  poles,  by  increasing  the  permeability  (/*)  of  the 
core  and  armature,  and  by  decreasing  the  average  lengths  (I)  of  the 
core,  the  armature,  and  the  air  gaps. 

When  it  is  considered  that  the  permeability  of  iron  is  much 
greater  than  that  of  air,  it  will  be  seen  that  the  force  of  attraction 
would  be  greatly  lessened  if  a  piece  of  the  iron  core  were  removed 
from  the  top.  The  force  exerted  by  a  horseshoe  electro-magnet 
is  much  greater  than  that  exerted  by  two  parallel  straight  electro- 
magnets corresponding  to  the  two  legs  of  the  horseshoe. 

654.  The  Morse  Telegraph  System.— The  fact  that  an 
electro -magnet  loses  its  magnetism  as  soon  as  the  exciting  current 
is  discontinued,  was  made  use  of  by  Professor  Morse  in  the  construc- 
tion of  his  system  of  electric  telegraph.  In  this  system  an  oper- 
ator at  one  station  can,  by  making  and  breaking  a  current  of  elec- 
tricity which  traverses  a  wire  to  a  second  station,  produce  or  de- 
stroy, at  will,  the  magnetism  of  an  electro-magnet  in  the  second 
station.  This  electro-magnet  is  a  part  of  an  instrument  called  a 
register,  which  will  be  described  later.  According  as  the  magnet 
is  excited  for  a  longer  or  shorter  interval,  the  register  marks  upon 
a  moving  band  of  paper  a  series  of  dashes  or  dots.  These  may  be 
combined  so  as  to  serve  as  an  alphabet. 

The  Morse  circuit  has  four  elements :  A  battery  to  produce  a 
current ;  a  key  to  manipulate  the  current ;  a  register  or  sounder  to 
record  the  current  thus  manipulated  ;  and  a  line  to  convey  the 
current. 

The  battery  generally  employed  is  a  modification  of  the  Dan- 
iell's  type,  called  the  Gravity  Battery  (Art.  635).  Dynamos  are, 
however,  rapidly  supplanting  them  in  the  large  telegraph  systems. 

The  key  for  manipulating  the  current  consists  of  a  lever,  B 
(Fig.  368),  and  anvil,  C,  both  of  brass,  and  insulated  from  each 

FIG.  368. 


other.  The  anvil  is  connected  to  one  terminal  of  the  line,  say 
from  the  battery,  and  B  to  the  other  terminal,  where  it  leaves  for 
the  receiving  station.  The  end  of  B  is  depressed  by  the  finger  of 


416 


ELECTRICITY     AND     MAGNETISM. 


the  operator  on  the  insulating  button  F,  and  is  raised  by  the  spring 
E,  when  the  pressure  is  removed.  The  former  movement  closes 
the  circuit,  the  latter  opens  it,  and  by  a  succession  of  these  the 
message  is  sent.  When  the  key  is  not  in  use,  the  brass  bar  K, 
hinged  to  the  base  of  B,  is  pressed  into  contact  with  C.  This 
closes  the  circuit  so  that  other  operators  on  the  line  may  have  a 
continuous  circuit  when  they  desire  to  send  a  message.  When  not 
in  use,  the  line  is  traversed  by  a  current. 

The  register  for  recording  the  message  on  paper  is  constructed 
as  follows  : 

The  lever  E  is  furnished  with  a  style  e  (Fig.  369),  directly  over 
which  is  a  groove  on  the  surface  of  a  solid  brass  roller  c.  Between 
c  and  e  is  a  long  paper  ribbon  E  R.  Attached  to  E  is  a  soft  iron 
armature  A,  placed  above  the  magnet  M,  and  furnished  with  a. 

FIG.  369. 


spring  s  to  raise  it  as  far  as  the  screw  i  allows  when  it  is  not  at- 
tracted by  M.  When  the  circuit  is  closed,  A  is  attracted  and  e 
rises  and  forces  the  paper  into  the  groove,  producing  a  slight  ele- 
vation on  its  upper  surface.  The  ribbon  is  pulled  along  at  a  uni- 
form rate  in  the  direction  of  the  arrow  by  clockwork  (not  shown 
in  the  figure),  so  that  when  the  circuit  remains  closed  for  a  little 
time,  a  dash  is  marked  on  the  paper  by  e  ;  when  it  is  closed  and 
instantly  opened,  the  result  is  a  dot — or  rather  a  very  short  dash. 
Spaces  are  left  between  these  whenever  the  circuit  is  opened. 
Combinations  of  these  dots,  dashes,  and  spaces,  all  carefully  regu- 
lated in  length,  compose  the  letters  of  the  alphabet.  Spaces  are 
also  left  between  the  letters,  and  longer  ones  between  words. 

By  lengthening  the  circuit  wire,  it  is  evident  that  the  person 
who  sends  the  message  at  n  p,  and  the  one  who  receives  it  at  E, 
may  be  miles  apart,  and  the  transmission  will  be  almost  instanta- 
neous, owing  to  the  rapid  passage  of  the  current. 

It  has  been  found  that  the  ear  is  sufficiently  accurate  to  allow 
of  the  dispensing  with  the  register,  as  used  by  Morse.  Instead  of 


THE    RELAY. 


41T 


It  a  sounder  is  employed.     In  this  the  end  of  the  lever  L'  (Fig.  370), 
instead  of  being  furnished  with  a  style,  is  made  to  strike  against 

FIG.  370. 


ihe  two  screws,  N't  0'.  The  downward  click  is  a  little  louder  than 
the  upward  one,  and  so  the  beginning  and  end  of  each  dot  or 
dash  are  distinguished  from  each  other.  Many  operators  learn 
from  the  first  to  read  by  the  ear,  and  have  never  used  a  register. 

For  a  line  it  was  at  first  supposed  that  a  complete  metallic  cir- 
cuit was  necessary,  hence  a  return  wire  was  employed.  But  this 
was  rejected  when  it  was  found  that  the  earth  could  be  used  as  a 
part  of  the  circuit,  as  shown  in  Fig.  371,  in  which  the  dotted  line 
and  arrow  beneath  the  surface  are  not  intended  to  convey  the  idea 
that  a  current  actually  flows  from  one  earth-plate  to  the  other,  but 

FIG.  371. 


that  a  complete  circuit  is  formed,  the  earth  acting  the  part  of  an 
infinite  reservoir  of  electricity.  S  and  Sf  are  the  terminal  stations, 
and  s  is  one  of  the  way  stations  which  may  occur  anywhere  along 
the  line.  At  every  station  both  a  key,  (7,  and  sounder,  1,  are  in- 
troduced into  the  circuit,  so  that  messages  can  be  both  sent  and 
received. 

655.  The   Relay. — When  a  telegraph  line  is  very  long,  its 
^resistance  is  high  and  the  leakage,  because  of  insufficient  iusula- 


UNIVERSITY 


418  ELECTRICITY    AND    MAGNETISM. 

tion,  is  great.  Hence  a  current  sufficiently  strong  to  satisfactorily 
operate  a  register  or  sounder  cannot  be  economically  sent  through 
it.  Accordingly  use  is  made  of  a  relay.  In  this  instrument  (Fig. 
372)  the  line  current  entering  at  W  and  leaving  at  W"  excites  the 
electro-magnet  M.  This  attracts  the  armature  A  of  the  delicately 
adjusted  lever  L.  The  adjustment  is  obtained  by  regulating  the 
tension  exerted  by  the  spiral  spring  s.  During  the  passage  of  a 
current  along  the  line,  the  lever  L  plays  lightly  to  and  fro,  but 
with  insufficient  strength  to  act  as  a  register  or  sounder.  It  can, 
however,  be  made  to  act  as  a  key  for  a  separate  local  circuit  in  the 
receiving  office.  One  terminal  of  this  local  .circuit,  which  contains- 
a  sounder  and  battery,  is  connected  by  the  binding-post  I  with  the' 


lever  L.  The  other,  through  n,  is  connected  with  the  screw  N. 
When  the  distant  operator  closes  his  key  the  armature  A  causes 
the  lever  L  to  close  the  local  circuit  at  N.  When  the  distant 
operator  opens  his  key,  the  spring  s  opens  the  local  circuit.  Thus 
the  moving  lever  of  a  relay  acts  as  a  key  for  a  local  circuit. 

Evidently  the  relay  may  be  used  for  repeating  a  message  on 
another  long  circuit. 

656.  Duplex  Telegraphy. — In  the  Morse  system  just  de- 
scribed evidently  but  one  message  can  traverse  the  wire  at  the 
same  time.  If  two  could  simultaneously  traverse  it,  the  earning 
capacity  of  the  line  would  be  doubled.  This  feat  can  be  accom- 
plished, and  is  termed  duplex  telegraphy.  A  simple  duplex  system, 
employing  the  principle  of  Wheatstone's  bridge  (Art.  646),  is 
shown  in  Fig.  373,  which  represents  two  stations  connected  by 
the  line  wire  L  L'.  C  L  R  is  a  W'heatstone  bridge,  modified  to 
suit  the  conditions  of  the  case,  I  the  sounder,  R  resistance  coils,  k 
a  key  working  upon  the  centre  and  having  forward  and  back  con- 


DUPLEX    TELEGRAPHY. 


419 


tacts  at  a  and  c,  b  the  battery,  and  E  the  earth  connections.     The 
same  letters,  accented,  represent  like  parts  at  the  second  station. 

FIG.  373. 


When  not  in  use  the  keys  make  back  contact  by  the  action  of  a 
spring.  The  ratio  of  the  resistance  C  R  and  R  E3  is  made  equal  to 
that  of  C  L  and  the  line  wire  L  L',  including  the  back  contact  earth 
connection  at  the  second  station.  When  thus  balanced  any  current 
arriving  at  C,  which,  dividing,  passes  through  C  L  L'  and  C  R  E3, 
will  maintain  the  points  L  and  R  at  the  same  potential. 

If  now,  a'  being  closed,  a  be  closed,  a  current  will  flow  through 
a  and  k  to  <7,  where  it  will  divide,  one  part  going  to  earth  through 
R  and  E3,  and  the  other  through  L  L'.  As  the  potentials  were 
made  equal  at  L  and  R,  no  current  will  pass  through  the  indicator 
/;  that  part  of  the  current  which  flows  through  L  L'  divides  at  L', 
part  going  through  C'  k'  a'  to  E",  and  part  through  /'  (giving 
signal)  and  R'  to  E'.  Thus  the  closing  of  a  gives  a  signal  at  /' 
but  none  at  I. 

If  now  the  second  operator  should  close  his  key  while  a  was 
closed,  a  current  from  b'  would  flow  through  c'  and  k'  to  C',  where 
it  would  divide,  part  going  to  earth  through  R'  and  E'  (joining 
the  current  already  flowing  through  from  L  L'),  and  part  would 
flow  to  L'  and  oppose  the  current  from  the  other  station;  this 
opposing  current  will  have  the  same  effect  as  increased  resistance 
in  the  line  wire  L  L',  and  hence  the  balance  C  L  R  will  be  dis- 
turbed, the  potential  of  L  rising  above  that  of  R,  and  resulting  in 
a  current  from  L  through  /  to  R,  giving  a  signal  at  /.  Thus  the 
register  at  each  station  will  respond  to  the  key  of  the  other,  and 
only  to  that,  whether  one  or  both  operators  be  signalling. 

The  above  explanation  of  the  principle  of  this  particular  mode 
of  sending  simultaneous  messages  in  opposite  directions  on  a 
single  wire,  does  not  pretend  to  describe  the  actual  arrangement 
of  wires  or  earths  in  use.  For  a  full  description  of  the  various 
modes  of  duplex  and  quadruple!  telegraphy  the  student  is  referred 
to  works  on  practical  telegraphy. 


420 


ELECTRICITY     AND    MAGNETISM 


657.  Atlantic  Telegraph  Cable.  — This  cable  stretches  a 
distance  of  3,500  miles,  and  from  the  nature  of  the  case  is  a  con- 
tinuous wire,  so  that  it  cannot  be  advantageously  worked  by  the 
Morse  apparatus.     The  indicator  employed  is  a  sensitive  galva- 
nometer needle,  which  is  made  to  oscillate  on  opposite  sides  of  the 
zero  point  by  the  passage  through  it  of  currents  in  opposite  direc- 
tions.    But  to  reverse  the  direction  of  the  current  throughout  the 
whole  length  of '  the  cable  is  a  slow  process.     For  the  cable  is  an 
immense  Ley  den  jar,  the  surface  of  the  copper  wire  (amounting  to 
425,000  sq.  feet)  answering  to  the  inner  coating,  the  water  of  the 
ocean  to  the  outer",  and  the  gutta-percha  between  the  two  to  the 
glass  of  an  ordinary  jar.     A  current  passing  into  it  is  therefore  de- 
tained by  electricity  of  the  contrary  kind  induced  in  the  water,  and 
no  effect  will  be  produced  at  the  farther  end  until  it  is  charged. 

This  very  circumstance,  at  first  considered  a  misfortune,  is 
now  taken  advantage  of  in  a  very  simple  and  ingenious  manner  to 
facilitate  the  transmission  of  signals.  The  current  is  allowed  to 
pass  into  the  cable  till  it  is  charged — then,  urithout  breaking  the 
circuit,  by  depressing  a  key  for  an  instant,  a  connection  is  made 
between  it  and  a  wire  running  out  into  the  sea ;  that  is,  between 
the  inner  and  outer  coatings.  This  partially  discharges  it,  and 
the  needle  at  the  other  end  is  deflected.  When  the  key  is  raised 
the  discharge  ceases,  the  current  flows  on  as  before,  and  the 
needle  is  deflected  in  the  opposite  direction. 

658.  Electric  Bells.— The  ordinary  electric  house  bell  con- 
sists of  an  electro-magnet,  which  moves  a  hammer  backward  and 

FIG.  374. 


forward  by  alternately  attracting  and  releasing  it,  so  that  it  beats 
against  a  bell.     The  arrangements  of  the  instrument  are  shown  in 


GALVANOMETERS.  421 

3?ig.  374.  A  current  from  a  battery  (usually  of  the  Leclanche 
pattern),  after  traversing  the  electro-magnet  Et  enters  a  spring 
attached  to  the  armature  and  bell-hammer.  It  leaves  the  spring 
by  an  adjustable  screw,  C,  and  returns  to  the  battery.  When  it 
flows  it  excites  the  magnet  which  attracts  the  armature  and  causes 
the  hammer  to  hit  the  bell.  In  moving  toward  the  magnet  the 
•contact  at  G  has  been  broken,  and  the  magnet  losing  its  magnetism 
allows  the  armature  to  spring  back  so  that  the  contact  is  renewed. 
This  operation  is  repeated,  the  current  repeatedly  making  and 
breaking  itself.  One  of  the  wires  from  the  battery  to  the  bell  is 
•cut  at  the  point  P,  and  a  push  button  is  inserted.  This  is  shown 
in  section  to  the  right.  An  insulating  knob,  P,  when  pressed, 
brings  a  spiral  spring,  which  is  connected  with  one  end  of  the  cut 
wire,  into  contact  with  the  other  end.  The  circuit  being  closed 
thus,  the  bell  commences  to  ring. 

659.  Galvanometers. — These  instruments  are  employed  in 
the  laboratory  for  the  determination  of  nearly  all  electrical  magni- 

FIG.  375. 


tudes.  They  serve  to  detect  the  presence  of  electrical  currents 
and  to  determine  their  strengths  and  directions.  The  principle  of 
their  action  is  electro-magnetic.  Suppose  a  magnetic  needle  (Fig. 
375),  free  to  move  about  a  pivot,  to  lie  in  the  direction  of  the 
earth's  magnetic  meridian.  Suppose  further,  that  it  be  surrounded 
by  a  coil  of  wire,  whose  windings  are  parallel  to  the  axis  of  the 
needle.  If,  now,  an  electrical  current  be  sent  through  the  coil,  it 
will  develop  magnetic  polarity  in  the  coil  so  that,  e.g.,  its  east  side 
will  be  equivalent  to  a  north  pole  and  its  west  side  to  a  south  pole. 
The  needle  will,  under  this  influence,  tend  to  place  itself  in  an  east 
and  west  direction.  It  will  not  quite  attain  this  direction,  for  it  is 
influenced  by  the  earth's  magnetism  at  the  same  time,  and  this 
tends  to  keep  it  in  the  meridian.  Upon  reversing  the  direction  of 
the  current,  the  polarities  of  the  sides  of  the  coil  become  reversed, 
and  the  needle  turns  so  that  its  poles  project  from  opposite  sides 


422  ELECTRICITY    AND     MAGNETISM. 

of  the  coil.  The  side  toward  which  the  north  end  of  the  needle 
turns  determines  the  direction  of  the  current  in  a  given  galvano- 
meter. The  angle  through  which  the  needle  is  deflected  deter- 
mines the  strength  of  the  current  flowing. 

TANGENT  GALVANOMETEKS. — If  the  wire  of  a  galvanometer  be 
wound  on  the  circumference  of  a  ring,  whose  diameter  is  at  least 
twelve  times  the  length  of  the  needle  at  its  centre,  the  strengths  of 
currents  causing  different  deflections  will  be  proportional  to  the 
tangents  of  the  corresponding  angles  of  deflection.  Such  an  in- 
strument is  called  a  tangent  galvanometer.  The  reason  for  having  a 
large  diameter  for  the  coil  is  that  those  of  its  lines  of  force,  which 
are  cut  by  the  short  needle  in  its  excursions,  are  then  straight  and 
perpendicular  to  the  earth's  lines.  The  magnet's  pole  is  thus 
moved  under  the  influence  of  two  forces,  which  act  continuously  at 
right  angles  to  each  other.  The  law  of  the  tangents  then  follows. 

REFLECTING  GALVANOMETERS. —  In  refined  laboratory  measure- 
ments the  determination  of  a  needle's  deflection,  by  observing  the 
movement  of  a  pointer  over  a  divided  scale,  is  inaccurate  and  in- 
convenient. Instead,  a  small  mirror  is  attached  to  the  magnet  and 
the  deflections  are  measured  by  the  different  divisions  of  a  sta- 
tionary divided  scale,  which  are  reflected  from  the  mirror  into  a 
stationary  telescope.  The  arrangement  is  shown  in  Fig.  319. 

A  method,  much  used  in  England,  is  to  have  the  mirror  reflect 
a  ray  of  light  from  a  small  hole  in  an  opaque  chimney  of  a  lamp 
upon  a  stationary  scale.  The  method  is  very  inconvenient,  as  it  re- 
quires the  observations  to  be  made  in  a  darkened  room.  The  ac- 
curacy to  be  obtained  is  not  as  great  as  by  means  of  a  telescope 
and  scale. 

BALLISTIC  GALVANOMETERS. — In  many  determinations  it.  is  re- 
quired to  measure  currents  which  last  but  for  an  instant,  or  to 
measure,  q uantities  of  electricity.  The  difficulties  connected  with 
these  determinations  are  much  lessened  if  the  time  required  by 
the  galvanometer  needle  to  make  a  single  oscillation  be  very  great, 
as  compared  with  the  time  occupied  by  the  electricity  in  passing. 
Thus  galvanometers  whose  needles  have  periods  of  from  five  to 
twenty-five  seconds  are  used,  and  are  called  ballistic  galvanometers. 

DIFFERENTIAL  GALVANOMETERS. — These  instruments  are  supplied 
with  two  sets  of  coils,  which  are  so  placed  that  they  will  produce 
the  same  electro-magnetic  effect  upon  the  single  needle,  providing 
they  be  traversed  by  currents  of  the  same  strength  and  direction. 
By  means  of  this  instrument  a  current  in  one  coil  may  be  brought 
to  a  given  strength  by  being  made  to  neutralize  the  effect  upon 
the  needle  from  another  current,  which  is  of  constant  (the  required) 
strength  and  passes  through  the  other  coil  in  an  opposite  direction. 


CHAPTER   VII. 


FIG.  376. 


ELECTRO-DYNAMICS. 

660.  Movement  of  Conductors  Carrying  Currents.— In 

the  preceding  chapter  it  has  been  shown  that  a  conductor  carrying 
an  electrical  current,  and  placed  in  the  vicinity  of  a  magnet,  tends 
to  move  the  magnet,  so  that  the  lines  of  force  from  each  may  be- 
come parallel,  or,  if  the  magnet  be  stationary,  the  conductor  strives 
to  move,  to  attain  the  same  end.  As  might  be  expected,  two 
neighboring  conductors,  while  traversed  by  currents,  tend  to  move 
so  as  to  render  their  lines  of  force  parallel. 

Without  any  knowledge  of  the  existence  or  properties  of  lines 
of  force,  Ampere,  in  1821,  arrived,  by  experiment,  at  the  following 
laws,  which  could  easily  have  been  predicted  by  such  a  knowledge. 

661.  Parallel  Currents.— 

1.  If  galvanic  currents  flow  through  parallel  wires  in  the  same 
direction,  they  attract  each  other ;  if  in  opposite  directions,  they 
repel  each  other.  These  ef- 
fects are  shown  by  suspend- 
ing wires,  bent  as  in  Fig. 
376,  so  that  their  lower  ends 
may  dip  into  four  separate 
mercury  cups,  a,  b,  a',  b',  by 
means  of  which  connection 
between  the  wires  C  and  D 
land  the  battery  may  be 
readily  made.  The  sus- 
pending threads  should  be 

two  or  three  feet  long,  and  the  mercury  cups  should  be  large 
enough  to  allow  considerable  lateral  movement  of  the  wires.  If 
simultaneous  currents  be  sent  through  the  two  wires  G  and  D,  in 
the  same  direction,  the  wires  will  move  toward  each  other;  if 
currents  be  sent  through  the  wires  in  opposite  directions  at  the 
same  time,  they  will  separate  more  widely. 

Hence,  when  a  current  flows  through  a  loose  and  flexible  helix, 
each  turn  of  the  coil  attracts  the  next,  since  the  current  moves  in  the 
same  direction  through  them  all.  In  this  way  a  spiral  suspended 
above  a  cup  of  mercury,  so  as  to  just  dip  into  the  fluid,  will  vibrate 
up  and  down  as  long  as  a  current  is  supplied.  The  weight  of  the 
helix  causes  its  extremity  to  dip  into  the  mercury  below  it ;  this 
closes  the  circuit,  the  current  flows  through  it,  the  spirals  attract 


424 


ELECTRICITY    AND    MAGNETISM. 


each  other,  and  lift  the  end  out  of  the  mercury ;  this  breaks  the 
circuit,  and  it  falls  again,  and  thus  the  movement  is  continued. 

2.  If  currents  flow  through  two  wires  near  each  other,  which 
are  free  to  change  their  directions,  the  wires  tend  to  become  paral- 
lel to  each  other,  with  the  currents  flowing  in  the  same  direction. 
Thus,  two  circular  wires,  free  to  revolve  about  vertical  axes,  when 
currents  flow  through  them,  place  themselves  by  mutual  attrac- 
tions in  parallel  planes,  as  in  Fig.  377,  or  in  the  same  plane,  as  in 


FIG.  378. 


Fig.  378.  In  the  latter  case,  we  must  consider  the  parts  of  the 
two  circuits  which  are  nearest  to  each  other  as  small  portions  of 
the  dotted  straight  lines,  c  d  and  ef. 

It  appears,  therefore,  that  galvanic  currents,  by  mutual  attractions 
and  repulsions,  tend  to  place  themselves  parallel  to  each  other  in  such 
a  manner  that  the  flow  is  in  the  same  direction. 

The  force  exerted  between  two  parallel  portions  of  circuits  is 
proportional  to  the  product  of  the  current  strengths,  to  the  length 
of  the  portions,  and  inversely  proportional  to  the  distance  between 
them.  The  force  exerted  by  each  current  acts  in  a  direction  per- 
pendicular to  the  direction  of  the  current. 


662.  Currents  not  Parallel. — Currents,  both  of  which  flow 
toward  a  common  point,  or  both  of  which  flow  away  from  a  common 
point,  attract  each  other. 

If  one  of  two  currents  flows  toward,  and  the  other  away  from  a 
common  point,  the  two  currents  repel  each  other. 

These  cases  are  evident  deductions  from  the  preceding  para- 
graph. Suppose  the  two  currents  (Fig.  379)  to  flow  in  A  and  B 
as  though  they  came  from  <?,  then  the  tendency  of  the  wires  A  and 
E  is  towards  parallelism,  and  as  we  suppose  the  currents  to  flow 
from  the  direction  C,  the  wires  must  tend  to  move  toward  each 


ELECTRODYNAMIC    ROTATION. 


other  in  order  to  become  parallel.  The  same  effect  would  be  pro- 
duced if  the  currents  in  A  and  B  were  to  flow  towards  C.  But  if 
the  current  in  A  flows  from 

the  direction  C7,  and  that  in  B  FIG.  379. 

towards  the  point  C,  then  the 
tendency  of  the  wires  to  be- 
come parallel,  with  the  cur- 
rents flowing  in  the  same 
direction,  causes  B  to  revolve 

about  C  as  a  centre  till  it  reaches  the  position  B'y  and  then  the 
condition  that  the  currents  shall  flow  in  the  same  direction  will  be 
fulfilled.  It  is  not  necessary  that  we  should  regard  A  and  B  as  ly- 
ing in  the  same  plane. 

A  sinuous  current  produces  the  same  effect  as  a  straight  cur- 
rent having  the  same  general  direction  and  length.  If  a  conductor, 
having  one  portion  sinuous  and  the  other  straight,  be  bent  as  in 
Fig.  380,  so  that  the  current  may  flow  from  a  to  b  through  the 

FIG.  380 


FIG.  381. 


straight  part,  and  from  b  to  c  through  the  sinuous  part,  the  two- 
portions  of  the  current  thus  flowing  close  together  in  opposite  di- 
rections, the  joint  electro-dynamic  effect  upon  a  movable  conductor 
parallel  to  a  b  will  be  inappreciable. 

663.  Continuous  Rotation  Produced  by  Mutual  Action 
of  Currents. — Suppose  a  continuous  current  to  flow  through  a 

wire  A,  as  indicated  in  Fig. 
381,  and  that  a  wire  B,  so 
bent  as  to  dip  into  the  mer- 
cury cup  m  at  one  end,  and 
into  the  annular  mercury 
trough  n  at  the  other,  be 
suspended  at  the  middle,  a 
counterpoise,  C,  keeping  it 
balanced. 

If,  now,  a  current  be  made 
to  flow  from  the  cup  w, 
through  B,  and  thence  out 
again  by  means  of  the  mercury  contact  in  n,  the  wire  B  will  rotate 
in  a  direction  opposite  to  that  of  the  current  in  A  ;  for  the  current 
in  B,  and  that  in  the  part  of  A  to  the  right  of  n,  are  both  flowing 
towards  n  and  hence  attract,  while  the  current  in  B  and  that  part 


426 


ELECTRICITY    AND    MAGNETISM 


of  the  current  in  A  immediately  to  the  left  of  n  are  flowing  in 
directions  to  cause  repulsion. 

A  beautiful  experiment,  illustrating  continuous  rotation,  is  to 
place  a  round,  shallow  dish,  containing  mercury,  on  the  pole  of  a 
vertical,  straight  electro-magnet.  Excite  the  magnet  and  dip  the 
terminals  of  a  circuit,  carrying  a  strong  current,  into  the  mer- 
cury at  the  centre  and  side  of  the  dish  respectively.  A  portion  of 
the  mercury  carries  the  current  from  the  centre  to  the  edge  of  the 
dish.  In  doing  so  it  is  made  to  rotate  by  the  action  of  the  lines  of 
force  from  the  magnet.  As  soon  as  it  has  rotated  a  new  portion 
of  the  mercury  is  made  to  carry  the  current.  This,  in  turn,  gives 
way  to  another  portion,  and  the  whole  body  of  mercury  is  soon  set 
into  rapid  rotation.  Centrifugal  force,  resulting  from  the  rotation, 
causes  the  mercury  to  heap  up  around  the  edges  of  the  dish,  and 
to  be  depressed  at  the  centre. 


FIG.  382. 


664.  Electro-dynamometer. — This  instrument,  invented  by 
Weber,  is  used  for  measuring  the  strengths  of  electrical  currents. 
Its  action  depends  upon  the  electro-dynamic  attractions  discussed 
in  Art.  661.  The  principles  of  its  construction  are  shown  in  the 
•crude  apparatus  represented  in  Fig.  382.  This  consists  of  a  fixed 
hollow  coil  of  wire,  in  the  centre  of  which 
is  suspended  another  smaller  coil.  The 
suspension  is  made  by  means  of  two  fine 
parallel  wires,  placed  one  or  two  milli- 
metres from  each  other.  The  upper  ends 
of  these  wires  are  connected  to  two  in- 
sulated binding-posts,  and  the  lower  ends 
are  connected  with  the  terminals  of  the 
suspended  coil.  The  suspension  is  so 
arranged  that,  when  no  current  is  pass- 
ing through  the  dynamometer,  the  planes 
of  the  two  coils  are  perpendicular  to  each 
other.  If,  now,  a  current  of  electricity 
be  sent  through  the  apparatus  (in  the  fol- 
lowing order  •  through  the  external  coil, 
down  one  suspension  wire,  through  the 
inner  coil  and  up  the  other  suspension 
wire),  the  suspended  coil  will  turn  and 
strive  to  cause  a  parallelism  of  the  planes 

and  currents  of  both  coils.  The  turning  force  of  the  currents  is 
resisted  by  an  increasing  force  exerted  by  the  twisted  wire  sus- 
pension. With  a  certain  current  the  coil  will  be  deflected  a 
certain  amount — i.e.,  until  the  two  opposing  forces  are  equal. 


INDUCED     CURRENTS.  427 

With  a  stronger  current  the  deflection  will  be  greater.  Thus  the 
magnitude  of  the  deflection  can  serve  as  a  measure  of  the  current 
strength. 

A  peculiarity  of  the  electro-dynamometer  is  that  it  serves  to 
measure  alternating  currents,  i.e.,  those  which  change  their  direc- 
tion, perhaps,  several  thousand  times  per  minute,  equally  as  well 
as  continuous  currents.  A  change  in  the  direction  of  flow  of  the 
main  circuit  changes  the  direction  in  both  coils.  This  does  not 
alter  the  direction  of  the  deflection. 


CHAPTER    VIII. 

ELECTRO-MAGNETIC    INDUCTION. 

665.  Currents  of  Electricity  Produced  by  Induction. — 
It  has  been  shown  that  when  a  current  of  electricity  flows  through 
a  conductor  the  air  or  other  dielectric  which  surrounds  the  con- 
ductor is  traversed  by  lines  of  force.     The  presence  of  these  lines 
indicates  that  the  dielectric  is  under  some  sort  of  a  strain.     To  pro- 
duce this  strain  energy  must  have  been  expended  by  the  current 
when  it  commenced  to  flow.     During  the  short  time  that  the  strain 
is  being  produced  there  is  an  opposition  to  the  exciting  current, 
which,  is  equivalent  to  a  current  in  an  opposite  direction.     Now,  it 
is  reasonable  to  suppose  that,  if  lines  of  force  or  a  magnetic  field 
be  produced  by  some  agency  around  a  closed  circuit  which  is 
primarily  traversed  by  no  current,  a  current  will  be  produced  in 
this  circuit.     The  direction  will  be  opposite  to  that  which  would 
be  necessary  to  create  the  field,  and  will  last  only  for  the  time  nec- 
essary to  produce  the  strain.     Furthermore,  upon  destroying  the 
field  it  is  reasonable  to  suppose  that  the  energy  which  it  represents 
will  appear  as  a  current  in  the  same  direction  as  one  which  could 
produce  the  field.     These  suppositions  are  substantiated  by  experi- 
ment, as  was  first  shown  by  Faraday.     The  currents  are  called 
induced  currents    (not    to    be    confounded    with   induced   electro- 
static charges),  and  those  currents  whose  directions  are  the  same  as 
a  current  which  could  produce  the  field  are  termed  direct  currents, 
while  those  in  an  opposite  direction  are  called  inverse  currents. 

666.  Methods  of  Producing  the  Inducing  Field. — Inas- 
much as  induced  currents  are  produced  by  any  variation   in   the 
strength  of  the  field  around   the   conductor  which  carries  them, 
they  can  be  produced  either  by  varying  the  strength  of  the  field 


428 


ELECTRICITY    AND    M  AG  N  ETISM. 


FIG.  383. 


current  or  by  moving  the  conductor  into  fields  of  various  strengths, 
For  the  sake  of  clearness  suppose  that  we  are  supplied  with  the 

apparatus  represented  in 
Fig.  383.  c  is  the  primary 
coil  of  wire  which  produces 
the  field,  and  is  traversed 
by  a  current  from  the  bat- 
tery. The  secondary  coil,  in 
which  induced  currents  are 
to  be  produced,  is  repre- 
sented at  d.  Its  terminals 
are  connected  with  a  gal- 
vanometer, which  indicates 
the  presence  and  direction 
of  the  induced  currents. 
Now  suppose  that  c  be 
placed  inside  of  d.  Upon 
starting  the  current  in  c  an 
inverse  current  will  be  in- 
duced in  d,  and  upon 

stopping  it  a  direct  current  will  be  induced.  Permitting  the  cur- 
rent in  c  to  flow,  increasing  or  decreasing  its  strength  will  produce 
inverse  or  direct  induced  currents  respectively.  If  the  current 
strength  in  c  be  maintained  constant,  removing  the  coil  c  will  pro- 
duce a  direct  current,  and  replacing  it  an  inverse  induced  current. 
Induced  currents  may  also  be  produced  by  magnets.  Consider 
a  magnet  to  be  the  equivalent  of  a  solenoid  traversed  by  a  current 
(Art.  651).  Dispensing  with  the  battery  we  have  the  apparatus  in- 


FIG.  384 


FIG.  385. 


dicated  in  Fig.  384     An  inverse  current  will  be  induced  by  the  in- 
troduction of  the  magnet  into  the  secondary  coil,  and  a  direct  cur- 


SELF-INDUCTION.  429 

rent  upon  removing  it.  An  inverse  current  may  also  be  induced  by 
strengthening  the  field  of  a  magnet  which  is  stationary  within  the 
secondary,  by  bringing  a  piece  of  iron  near  to  it.  In  this  case  the  iron 
becomes  a  magnet  by  induction,  as  shown  in  Fig.  385,  and  adds  its 
lines  of  force  to  the  field.  Direct  induced  currents  will  follow  the 
removal  of  the  iron. 

It  is  well  to  remark  that,  as  motion  is  merely  relative,  it  is  im- 
material whether  a  magnet  be  placed  in  a  secondary  coil  or  the  lat- 
ter be  placed  around  the  magnet. 

The  facts  which  have  been  mentioned  may  be  summed  up  in  a 
single  law  : 

Inverse  induced  currents  always  result  from  an  Increase  in  the 
number  of  lines  of  force  which  pass  through  the  circuit,  and  Direct 
induced  currents  always  result  from  a  Decrease  in  the  number  of 
these  lines. 

667.  Lenz's  Law. — If  two  conductors,  A  and  B,  in  one  ofwhichf 
A,  a  current  is  flowing,  be  made  to  change  their  relative  positions,  then 
a  current  will  be  induced  in  B  in  a  direction  which  will  cause  a  mu- 
tual action  in  tlte  two  conductors  tending  to  oppose  their  motion. 
Thus,  if  A  and  B  be  brought  nearer  together  an  inverse  current  will 
flow  in  B,  and  currents  flowing  in  opposite  directions  repel  each 
other  ;  and  if  A  and  B  be  caused  to  move  apart,  then  a  direct  sec- 
ondary current  ^Yill  flow  in  B,  and  currents  flowing  in  the  same 
directions  will  attract  each  other.  This  statement  of  the  results  of 
experiments  will  aid  the  memory  in  regard  to  the  directions  of  the 
primary  or  secondary  currents. 

663.  Self-induction. — Whenever  a  current  is  started  in  a  coil 
of  wire,  lines  of  force  are  created  which  increase  in  number  from 
zero  to  a  maximum.  Owing  to  the  increase,  they  induce  cur- 
rents in  the  coil  which  are  opposite  to  the  direction  of  the  original 
current.  "Upon  stopping  the  original  current  the  lines  of  force 
decrease  in  number  and  thus  induce  a  direct  current  in  the  coil. 
The  induction  in  such  a  case  is  termed  self-induction,  and  the  cur- 
rents are  termed  extra  or  self-induced  currents. 

The  existence  of  self-induced  currents  may  be  demonstrated 
by  the  Wheatstone  bridge  combination  (Art.  646).  Let  three  of 
the  arms  of  the  bridge  be  made  up  of  resistances  without  self-in- 
duction (Art.  645),  the  fourth  arm  consisting  of  an  ordinary  unifilar 
coil.  For  the  purpose  of  increasing  the  self-induction  of  this  fourth 
arm,  insert  a  piece  of  soft  iron  in  the  coil.  Obtain  a  balance  in  the 
bridge  by  employing  a  constant  purrent.  When  a  balance  has 
been  obtained  the  galvanometer  will  show  no  deflection.  If .  the 


430  ELECTRICITY    AND     MAGNETISM. 

current  be  now  stopped,  the  current  induced  in  the  fourth  arm  will 
cause  a  deflection  of  the  galvanometer  needle. 

669.  Coefficients  of  Mutual  and  Self-induction.  —It  can 
be  proved  mathematically  that  the  electro-motive  force  induced  in  a 
closed  circuit  is  equal  to  the  rate  of  variation  of  the  number  of  lines 
of  force  which  pass  through  it. 

If  in  a  short  interval  of  time  dt,  the  number  of  lines  of  force  N 
increases  a  small  amount  dN,  then  the  electro-motive  force 

v          dN 

E  =  ~w 

will  be  induced  in  the  circuit  which  surrounds  these  lilies.  In  case 
two  coils,  a  primary  and  secondary,  be  fixed  in  position,  and  the 
strength  of  the  current  in  the  primary  be  increased  by  an  amount  do 
in  the  short  time  dt,  then  the  electro-motive  force 

w  nrdc 

E=~Mdt 

will  be  induced  in  the  secondary  during  that  time.  M  is  a  constant 
which  is  called  the  coefficient  of  mutual  induction  between  the  two 
coils.  Its  value  depends  upon  the  shape  and  number  of  windings 
of  wire  around  the  respective  coils  and  their  relative  positions.  It 
is  numerically  equal  to  the  number  of  absolute  lines  of  force  which 
would  be  sent  through  either  coil  when  an  absolute  unit  current  of 
electricity  was  sent  through  the  other  coil.  It  makes  no  difference 
which  coil  be  chosen  as  a  primary  in  determining  M. 

If  it  be  supposed  that  the  two  coils  be  made  to  coincide,  i.e., 
that  there  be  but  one  coil,  then  the  electro-motive  force  of  self- 
induction 


The  constant  L  is  called  the  coefficient  of  self-induction,  and  is 
equal  to  the  number  of  absolute  lines  of  force  which  a  coil  would 
send  through  itself  if  it  were  traversed  by  an  absolute  unit  of  current. 

670.  Induced  Currents  from  the  Earth.  —  If  a  coil  (whose 
terminals  are  connected  with  a  sensitive  galvanometer)  be  placed 
so  that  its  axis  is  parallel  with  the  axis  of  a  dipping-needle  (Art. 
621),  it  will  be  pierced  by  a  maximum  number  of  the  earth's  lines 
of  magnetic  force.  If  it  be  now  turned  through  90°  around  an 
axis  perpendicular  to  its  own  axis,  the  number  of  the  lines  piercing 
it  will  decrease  to  zero,  and  the  galvanometer  will  indicate  that  a 
current  is  being  induced  by  the  rotation. 

Continuous  variations  in  the  strength  of  the  earth's  magnetism 
sometimes  induce  currents  of  considerable  strengths  in  long  tele- 
graphic circuits.  Such  currents  are  known  as  earth  currents. 


OF  THE 

(UNIVERSITY 


INDUCTION    CfrJ41SjniAx'      431 


671.  Arago's  Rotations.  —  In  1824  Arago  observed  that  the 
collations  of  a  magnetic  needle  were  reduced  in  number  by  sus- 
pending a  copper  plate  above  it.     This  observed  phenomenon  soon 
led  him  to  the  discovery  that  if  a  horizontal  copper  disc  be  made 
to  rotate  rapidly,  a  magnetic  needle  suspended  above  it  would  ro- 
tate also.     This  effect  may  also  be  produced  with  other  metals 
though  in  less  degree. 

If  a  disc  of  copper  be  set  spinning  on  an  axis,  between  the 
poles  of  a  powerful  electro-magnet  whose  circuit  is  broken,  the  axis 
of  the  disc  being  parallel  to  the  lines  of  force,  the  rotation  con- 
tinues with  slight  loss  of  velocity  for  a  long  time  ;  but  if  the  circuit  be 
suddenly  closed  the  rotation  is  at  once  checked,  or  possibly  stopped. 
If  such  a  disc  be  kept  in  rapid  rotation  by  a  suitable  band  and 
pulley,  after  the  circuit  is  closed,  the  disc  will  be  heated  by  the 
action  of  the  magnet. 

These  effects  were  explained  by  Faraday  as  being  due  to  cur- 
rents induced  in  the  mass  of  metal.     Thus  let  a  needle,  N  S  (Fig. 
386),  be  suspended  above  a  metal  disc  A  B.     The  magnetic  cur- 
rents flow  around  the  needle  as  indicated  in 
the  figure,  the  currents  below  the  needle  from  FlG- 

right  to  left  as  shown  by  the  dotted  arrow,  and 
those  above  from  left  to  right,  as  shown  by  the 
full  arrow.  Now  suppose  the  disc  to  be  ro- 
tated in  the  direction  from  A  to  B  ;  the  por- 
tions of  the  currents  around  2V  8  which  are 
nearest  to  the  disc  will  induce  in  that  part 
of  the  disc  towards  A  currents  whose  direc- 
tions are  such  as  to  resist  the  motion  of  the 
disc,  according  to  Lenz's  law  (Art.  667),  that  is  to  say,  currents 
will  flow  in  the  disc  from  left  to  right  ;  while  in  that  part  of  the 
disc  towards  B,  which  is  moving  away  from  N,  the  induced  cur- 
rents are  from  right  to  left,  and  so  resist  the  motion  of  B  away 
from  N. 

If  the  needle  had  been  moved,  the  disc  remaining  fixed,  the 
same  analysis  of  the  motion  might  be  made,  and  we  should  find 
that  the  disc  would  resist  the  motion  of  the  needle.  A  copper  col- 
lar or  frame  is  sometimes  used  to  coil  the  galvanometer  wire  upon, 
in  order  to  reduce  or  damp  the  oscillations  of  the  needle,  and  bring 
it  more  quickly  to  rest. 

672.  Induction   Coils.  —  These   instruments   serve  to    trans- 
form currents  of  low  E.  M.  F.  into  alternating  currents  of  high  E 
M  F.     Their  forms  and  sizes  are  many,  and  only  their  principle 
need  be  mentioned  here.     A  continuous  current  of  low  E.  M.  F.  is 
passed  through  a  primary  coil  made  of  a  few  turns  of  coarse  insu- 


432 


ELECTRICITY    AND    MAGNETISM. 


FIG.  387. 


lated  copper  wire  (Fig.  387).  The  centre  of  the  coil  is  filled  witb 
a  core  of  soft  iron  wires.  Before  passing  through  the  coil  the  cur- 
rent traverses  some  sort 
of  a  current  -  breaker, 
e.g.,  the  one  shown  in 
the  cut  acts  upon  the 
same  principle  as  the 
breaker  of  the  electric 
bell  described  in  Art. 
658.  By  means  of  this 
breaker  the  current  in 
the  primary  is  rapidly 
made  and  broken.  Al- 
ternating currents  are  thus  induced  in  a  secondary  surrounding 
coil,  which  is  wound  with  many  turns  of  .very  fine  insulated  wire. 
The  E.  M.  F.  of  these  induced  currents  is  great  because  the  co- 
efficient of  mutual  induction  is  great.  This  is  owing  to  the  large 
number  of  turns  of  wire  in  the  secondary  and  to  the  presence  of 
the  iron  core.  Both  conspire  to  cause  a  large  number  of  lines  of 
force  to  pierce  the  circuit  during  the  short  interval  required  to 
make  the  circuit  of  the  primary. 

The  function  of  the  induction  coil,  as  here  given,  is  often  re- 
versed, in  which  case  it  becomes  what  is  termed  a  transformer. 
Transformers  are  much  used  in  the  commercial  distribution  of 
rapidly  alternating  currents  for  lighting  and  other  purposes.  Al- 
ternating currents  of  high  E.  M.  F.  and  low  current  strength  are 
received  from  a  main  line  into  the  finer  wire  coil  of  an  induction 
coil.  The  thick  wire  coil  of  the  transformer  is  connected  with  the 
customer's  home  circuit,  and  delivers  to  it  currents  of  great  strength 
but  at  low  potential. 

673.  The  Telephone. — This  instrument  for  reproduction  of 
sound  at  a  distance  by  means  of  electric  currents  is  shown  in  sec- 
tion in  Fig.  388,  in  which  a  a'  is  a  disc  or  diaphragm  of  thin  soft 
iron,  the  circumference  of 

which  is  firmly  clamped  FIG.  388. 

between  the  mouth  guard 
m  m'  and  the  case  n  ri, 
upon  the  centre  of  which 
the  sound-waves  from  the 
mouth  impinge,  as  at  Et 
and  communicate  to  it  vi- 
brations corresponding  to 

the  simple  or  composite  sounds  uttered.     These  vibrations  of  the 
disc  cause  a  continual  variation  in  the  distance  of  the  disc  fron> 


BLAKE    TRANSMITTER. 


433 


the  end  of  a  bar  magnet,  b.  Around  the  end  of  the  magnet  near- 
est to  the  diaphragm  a  a'  is  a  coil,  c  c',  of  fine  insulated  copper 
wire,  the  ends  of  which  are  connected  with  binding-posts,  d  d\ 
From  these  posts  are  carried  wires  to  another  precisely  similar 
instrument  at  the  station  with  which  communication  is  to  be  held. 
"When  a  word  is  spoken  into  the  instrument  at  E,  the  vibrations 
communicated  to  the  disc  a  a'  cause  variations  in  the  magnetic 
field  of  the  bar  6,  and  these  variations  induce  electric  currents 
which  flow  in  the  coil  c  c',  and  thence  through  the  connecting 
wires  to  the  coil  in  the  instrument  held  to  the  ear  of  the  listener, 
and  these  currents  in  the  last-named  coil  produce  variations  in 
the  strength  of  the  magnet  of  the  receiving  instrument,  causing 
precisely  the  same  vibrations  in  its  diaphragm  as  were  originally 
set  up  in  the  first.  The  vibrations  of  the  diaphragm  are  trans- 
mitted through  the  air  to  the  ear ;  and  though  no  sound  has  been 
transmitted  from  one  station  to  the  other,  the  words  spoken  into 
one  instrument  are  distinctly  delivered  by  the  other.  The  sound 
vibrations  are  the  cause  of  electric  currents,  and  these  in  turn 
finally  produce  sound  vibrations  again. 

To  such  perfection  of  action  have  these  instruments  been 
brought,  that  not  only  can  the  spoken  words  be  heard,  but  the 
peculiar  characteristics  of  voice  are  so  faitkfully  reproduced  that 
by  these  the  speaker  may  be  recognized. 

674.  The  Blake  Transmitter. — The  electro-motive  forces 
generated  by  the  moving  diaphragm  of  the  Bell  telephone  are 
not  sufficiently  large  to  produce 
satisfactory  results  on  long  lines. 
Therefore  an  instrument  termed  a 
transmitter  is  substituted  for  the 
telephone  at  the  sending  end  of 
the  line.  A  common  and  very 
satisfactory  form  of  transmitter 
is  one  designed  by  Francis  Blake. 
It  is  represented  in  Fig.  389,  and 
its  action  depends  upon  the  prin- 
ciple that  the  electrical  resistance 
offered  by  a  carbon  contact  varies 
greatly  with  the  pressure  exerted 
upon  it. 

The  sound  to  be  transmitted 
is  received  in  the  mouth-piece  M, 
which  causes  it  to  set  the  diaphragm  D  into  corresponding  vibra- 
tions. Touching  the  rear  of  the  diaphragm  is  a  platinum  or  car- 
'bon  point,  which  is  attached  to  a  piece  of  watch-spring,  aud  which 


FIG.  389. 


434  ELECTRICITY     AND     MAGNETISM. 

is  in  connection  with  one  terminal  of  a  battery,  B.  (This  battery- 
is  brought  into  circuit  only  as  the  transmitter  is  to  be  used.)  The 
point  forms  a  loose  contact,  C,  with  a  carbon  button,  which  is  also 
mounted  upon  a  spring.  The  current  from  the  battery  flows 
through  this  contact  to  the  rest  of  the  circuit.  As  the  diaphragm 
vibrates  it  causes  the  point  to  exert  correspondingly  different 
pressures  upon  the  button.  The  resistance  of  the  circuit  is  thus 
varied,  and  this  results  in  variations  in  the  current  which  are  the 
electrical  counterparts  of  the  sound  vibrations. 

A  Bell  receiver,  placed  in  the  same  circuit  with  the  battery  and 
transmitter,  will  yield,  besides  the  transmitted  sound,  a  disagreeable 
"  sizzling "  noise.  To  obviate  this  an  induction  coil,  /,  is  intro- 
duced. The  varying  current  from  the  battery  and  transmitter  is 
passed  through  the  primary  of  a  small  induction  coil,  and  the  line 
wires,  with  their  receivers  included,  are  connected  with  the  second- 
ary coil.  In  this  case  the  currents  on  the  line  flow  in  opposite 
directions  to  what  they  would,  if  connected  directly  with  the  trans- 
mitter circuit.  This,  however,  is  of  no  consequence. 

The  springs  of  the  transmitter,  which  bear  the  carbon  button 
and  platinum  point,  are  fastened  to  one  piece  of  brass,  but  are  insu- 
lated from  each  other.  The  amount  of  pressure  at  the  contact  is 
regulated  by  a  screw,  whose  end  tits  the  bent  end  of  the  brass 
holder.  The  holder  is  supported  by  pliable  spring  bands  which- 
are  attached  to  the  case  of  the  transmitter.  Although  this  method 
of  adjustment  is  simple  and  appears  crude,  the  delicacy  of  it  is- 
marvellous. 

675.  Dynamos. — These  machines  are  for  converting  mechani- 
cal energy  into  electrical  currents.  A  discussion  of  the  principles 
of  their  construction  is  here  out  of  place,  and  the  student  is  re- 
ferred to  some  one  of  the  many  technical  treatises  on  the  subject. 
The  principle  of  their  action  may  be  described. 

The  dynamo  has  two  essential  parts — a  movable  *  conductor, 
called  an  armature,  and  a  magnet,  in  whose  field  the  armature 
moves.  The  armature,  by  its  motion,  varies  the  number  of  the 
field  lines  which  pass  through  it,  and  is  therefore  traversed  by  in- 
duced currents. 

Fig.  390  (taken  from  S.  P.  Thompson's  "  Dynamo-Electric  Ma- 
chinery ")  represents  an  ideal  dynamo  in  its  simplest  form.  N  and 
S  are  the  poles  of  a  field  electro-magnet.  The  lines  of  force  pass 
between  the  poles  and  pierce  the  looped  conductor  C,  which  forms 
the  armature.  The  armature,  in  the  position  indicated  by  the  con- 

*  In  some  machines  the  armature  is  stationary  and  the  field  magnets  are- 
movable. 


DYNAMOS. 


435 


tinuous  lines,  is  pierced  by  a  maximum  number  of  the  field  lines  ; 
upon,  turning  through  90°,  coming  then  into  the  position  indicated 


FIG.  390. 


by  the  dotted  lines,  it  is  pierced  by  none  of  the  lines.  During 
the  whole  quarter  revolution  there  has  been  a  decrease  in  the  num- 
ber of  lines  passing  through  the  loop.  An  induced  current,  flow- 
ing in  a  certain  direction,  has  accompanied  the  movement.  During 
another  quarter  revolution  the  number  of  penetrating  lines  will  be 
on  the  increase,  but  they  now  pass  through  the  loop  in  an  oppo- 
site direction  to  what  they  did  before,  and  hence  the  induced  cur- 
rents which  result  from  the  increase  are  in  the  same  direction, 
referred  to  the  conductor,  as  during  the  first  quarter  revolution. 
During  the  next  two  quarter  revolutions  the  induced  currents  will 
flow  in  an  opposite  direction.  Thus  by  continuous  revolution  the 
armature  is  traversed  by  currents  which  reverse  their  directions 
twice  each  revolution. 

In  order  to  lead  the  currents  from  the  armature  into  a  circuit 
where  they  can  be  used,  and  in  order  to  rectify  them,  i.e.,  cause 
them  to  flow  in  the  same  direction,  use  is  made  of  a  commutator. 
Fig.  391  represents  a  two-part  commutator  suited  for  our  single- 
loop  armature.  It  consists  in  an  insulating 
cylinder,  to  be  applied  to  the  extremity  of  the 
axis  of  the  armature.  Upon  it  is  slid  a  metal 
tube  slit  into  two  parts.  To  each  part  is  con- 
nected one  of  the  ends  of  the  loop,  as  shown  in 
Fig.  390.  Against  the  commutator  are  pressed 
two  spring  brushes,  B  B,  which  are  connected 
with  the  two  terminals  of  the  outside  circuit 
respectively.  The  commutator  revolves  with  the  armature,  but 
the  brushes  remain  stationary.  Both  are  so  arranged  that  at  the 
instant  the  plane  of  the  loop  of  the  armature  passes  through 
the  vertical  plane,  the  brushes  will  slide  from  one  segment  of  the 
commutator  to  the  other.  At  this  instant  the  induced  current 
reverses  the  direction  of  its  flow,  and  the  commutator,  exchanging 


FIG.  391. 


4:36  ELECTRICITY     AND     MAGNETISM. 

the  connections  with  the  external  circuit,  causes  the  external  cur* 
rent  to  flow  in  one  direction. 

The  E.  M.  F.  which  could  be  obtained  from  such  an  ideal  dy- 
namo would  be  very  small.  To  increase  it,  the  total  number  of 
lines  of  force  which  are  passed  through  or  taken  out  of  the  circuit 
in  a  unit  time  must  be  increased.  There  are  three  \vajs  in  which 
this  may  be  accomplished :  the  speed  of  revolution,  the  number  of 
loops  in  the  armature,  or  the  strength  of  the  field  may  be  increased. 
It  need  not  be  considered  here  how  this  is  carried  out  in  practice. 

The  field  magnets  of  a  dynamo  may  be  excited  by  currents  from 
an  external  source,  by  the  whole  of  the  machine's  armature  current, 
or  by  only  a  portion  of  the  armature  current.  The  dynamos  are  then 
termed  separately  excited,  series,  or  shunt  machines  respectively. 

When  the  field  is  furnished  by  permanent  magnets  the  machine 
is  no  longer  termed  a  dynamo,  but  a  magneto-electrical  generator. 
Such  machines  are  not  a  commercial  success  except  in  the  very 
small  sizes. 

676.  Electric  Motors. — The  function  of  these  machines  is 
the  converse  of  that  of  dynamos.  They  are  intended  to  transform 
electrical  energy  into  motion.  The  dynamo  of  the  previous  article 
becomes  an  ideal  motor  by  simply  sending  through  it,  from  the  ex- 
ternal circuit,  a  current  in  an  opposite  direction.  The  commutator 
accomplishes  that  the  lines  of  force,  due  to  the  current  flowing  in 
the  armature,  shall  never  become  parallel  to  the  field's  lines.  In 
striving  to  secure  such  parallelism  the  armature  revolves  upon  its 
axis,  and  just  as  it  is  about  to  reach  the  goal  the  commutator  re- 
verses the  direction  of  its  lines,  and  it  moves  through  another  half 
revolution  to  be  again  frustrated  in  its  attempts. 


CHAPTER    IX. 

ELECTRO-CHEMISTRY    AND     ELECTRO-OPTICS. 

677.  Electrolytes. — Liquids  may  be  divided  into  three  classes, 
depending  upon  their  behavior  towards  the  electrical  current — 
those  which  do  not  conduct  at  all,  as  kerosene,  turpentine,  and  oils 
generally;  those  which  conduct  without  decomposition,  e.g.,  mer- 
cury and  molten  metals ;  those  which  are  decomposed  when  they 
conduct  a  current,  e.g.,  solutions  of  acids  or  metallic  salts  and  cer- 
tain fused  solid  compounds.  The  liquids  of  the  last  class  are 
called  electrolytes,  and  the  process  of  decomposing  an  electrolyte  by 


ELECTROLYSIS    OF    SALT    SOLUTIONS. 


43  r 


FIG.  392. 


means  of   an  electrical  current  is  termed  electrolysis.     The  two 
parts  into  which  the  electrolyte  is  decomposed  are  termed  ions. 

678.  Electrolysis  of  Sulphuric   Acid.  —  If  a  current  of 
electricity  flows  into  a  solution  of  sulphuric  acid  (H2SO4)  in  water 
by  means  of  an  electrode,  and  if,  after  traversing  the  solution,  it 
flows  out  through  another  electrode,  then  it  will,  by  its  passage, 
decompose  the  acid  into  two  parts — H2  and  SO4.     The  hydrogen 
will  appear,  in  the  form  of  gas  bubbles,  at  the  electrode  through 
which  the  current  makes  its  exit  from  the  solution.     The  SO4  will 
endeavor  to  appear  at  the .  electrode  where  the  current  entered, 
but  the  water  of  the  solution  seizes  upon  it,  and  together  they 
form  sulphuric  acid,  leaving,  however,  one  portion  of  oxygen  to 
appear,  as  gas,  at  the  electrode.     The  effect 

of  the  passage  of  the  current  is  to  virtually 
decompose  water  (H2O)  into  hydrogen  and 
oxygen,  there  .being  twice  as  much  of  the 
former  as  of  the  latter. 

Hoffmann's  apparatus  for  electrolyzing 
sulphuric  acid  is  shown  in  Fig.  392.  The 
dilute  acid  solution  is  poured  into  the  funnel 
F,  and  flowing  into  the  two  arms  of  the  front 
U-tube  fills  them,  providing  the  stop-cocks 
at  their  tops  be  opened.  After  filling,  the 
cocks  are  closed  and  a  current  is  made  to 
pass  between  the  two  platinum  electrodes  E 
E.  The  gases  which  are  evolved  at  the  elec- 
trodes rise  in  the  respective  tubes  above  them 
and  displace  the  liquid.  These  gases  are 
subjected  to  the  same  pressure  exerted  by 
the  liquid  in  the  funnel.  Their  volumes  may  be  read  off  from 
graduations  on  the  tubes  containing  them.  The  gases  may  be 
taken  off  through  the  cocks  and  their  natures  tested — the  oxygen 
being  made  to  relight  a  glowing  taper  and  the  hydrogen  being 
made  to  explode  when  mixed  with  air  in  a  test-tube. 

679.  Metallic  Salts. — When  the  electrolyte  is  a  metallic  salt 
solution  the  metal  will  be  deposited  at  the  electrode  where  the  current 
leaves  the  solution.     The  acid  of  the  salt  appears  at  the  other  elec- 
trode.    The  metal   may  be  deposited   upon   the   surface   of  the 
electrode  in  the  form  of  a  thin  metallic  film.     In  case  the  metal 
has  a  strong  affinity  for  the  water  of  solution,  e.g.,  sodium  in  water, 
it  will  go  into  solution  arid  hydrogen  will  be  evolved  as  a  secondary 
product.      It    is   nevertheless   true    that   Davy  obtained   metallic 
.sodium  and  potassium  by  the  electrolysis  of  strong  caustic  soda 


438  ELECTRICITY     AND    MAGNETISM. 

and  potash.  These  metals  may  be  obtained  by  electrolysis,  if  a 
mercury  electrode  be  employed.  They  then  appear  in  the  form  of 
amalgams. 

The  character  of  a  deposited  metal  often  varies  under  different 
current  strengths  or  different  concentrations  of  solution.  Copper 
may  be  deposited  in  the  form  of  a  black  powder  instead  of  an 
even  metallic  film.  Silver  may  appear  in  the  form  of  crystals. 
Platinum  generally  appears  as  a  black,  finely  divided  sponge.  Tin, 
from  tin  chloride,  forms  a  beautiful  "  tree "  of  tin  crystals,  the 
branches  spreading  out  gracefully  from  the  electrode. 

680.  Faraday's  Laws. — Faraday  proved  that  a  given  quan- 
tity of  electricity  always  deposits  the  same  weight  of  a  given  ion  from 
an  electrolyte  through  which  it  passes.     Thus  a  coulomb  of  elec- 
tricity always  deposits  .001118  gram  of  silver  on  an  electrode.     It 
makes  no  difference  whether  the  electrolyte  be  molten  silver  iodide 
or  chloride,  or  whether  it  be  a  water  solution  of  silver  nitrate,  sul- 
phate, acetate,  or  cyanide.     The  passage  of  one  coulomb  is  always 
accompanied  by  the  deposition  of  this  much  silver.     The  weights 
of  other  chemical  elements  which  a  coulomb  will  deposit  are  in  pro- 
portion to  their  chemical  equivalents     This  being  so,  it  must  be  con- 
cluded  that  a  given   quantity   of    electricity  ruptures  the    same 
number  of  molecular  valencies,  whatever  the  electrolyte  may  be. 

681.  Voltameters. — From  Faraday's  laws  it  will  be  readily 
seen  that  from  weighing  the  amount  of  an  ion,  which  is  deposited 
by  the  passage  of  a  certain  quantity  of  electricity,  this  quantity  may 
be  determined.     Thus,  if  a  certain  quantity  deposits  silver  on  an 
electrode  so  as  to  cause  it  to  weigh  1.118  gram  more  than  before 
the  passage,  it  is  evident  that  1,000  coulombs  have  passed.     If  the 
quantity  passed  in  the  form  of  a  constant  current,  which  lasted  for 
1  second,  then  the  current  strength  was  1,000  amperes.     For  an 
ampere  means  a  strength  of  current  which  delivers  1  coulomb  per 
second,  but  in  this  case  1,000  coulombs  were  delivered  in  a  second. 
In  general,  if  z  —  the  electro-chemical  equivalent  of  the  substance 
deposited,  i.e.,  grams  per  coulomb,  c  =  the  current  in  amperes, 
t  =  time  in  seconds  that  the  current  was  maintained,  the  weight 
of  the  substance  deposited 

w  —  c  z  t. 

In  case  w  and  t  are  measured,  the  current  strength  may  be  de- 
termined by  the  formula 

w 

c  =  ~t 

Instruments  for  measuring  current  strengths  in  this  manner  are 
called  voltameters.  The  substances  generally  employed  for  depo- 


ELECTROPLATING.  439. 

sition  are  copper  from  a  solution  of  its  sulphate,  silver  from  its 
nitrate,  and  hydrogen  from  dilute  H2SO4.  In  the  case  of  hydro- 
gen weighing  is  difficult,  hence  the  volume  is  measured  and  then 
reduced  to  760  mm.  pressure  and  0°  C. 

A  current  of  1  ampere  deposits  in  1  minute,  of 

Hydrogen  (at  760  mm.  and  0°  C.) 6.942  cu.  cm. 

Copper 01969  gram. 

Silver 06708  gram. 

Zinc 02018  gram. 

The  Edison  electrical  companies  place  zinc  voltameters  in  the 
houses  of  their  customers,  and  thus  measure  the  quantity  of  elec- 
tricity consumed. 

682.  Theory   of  Electrolysis. — The   most   satisfactory  ex- 
planation of  the  phenomena  of  electrolysis  is  embodied  in  the  the- 
ory of  Grotthuss,  somewhat  modified  by  Clausius.     The  molecules 
of  an  ordinary  solution  are  supposed  to  be  in  constant  vibration  in 
all  possible  directions.     Owing  to  collisions  between  the  molecules, 
or  other  causes,  the  constituent  atoms  are  constantly  leaving  their 
partners  and  combining  with  others  to  form  new  molecules.   Every 
molecule,  having  unit  valency,  is  charged   with  the  same  quantity 
of  electricity — half  being  positive  and  half  negative.     The  positive 
resides  on  one  ion  of  the  molecule  and  the  negative  on  the  other. 
Now,  upon  subjecting  the  solution  to  a  difference  of  potential  be- 
tween the  electrodes,  the  direction   of   the  molecular  motions  is 
controlled,   and  ions,  which  by  chance  are  isolated,  will  tend  to 
move  towards  one  or  the  other  electrode,  according  to  the  signs 
of  the  charges  which  are  upon  them.     If  the  impressed  electro- 
motive force  is  large  enough  to  prevent  recombination  of  these  ions, 
they  will  continue  their  movements  towards  the   electrodes,  and 
will  accumulate  around  them.     Upon  touching  the  electrodes  they 
impart  to  them  their  minute  charges  and  the  continuous  accumula- 
tion of  these  maintains  a  current  in  the  circuit. 

According  to  this  theory,  electrolytic  conduction  of  electricity 
is  similar  to  the  convection  of  heat  in  liquids.  The  transportation 
of  electricity  is  accompanied  by  a  transportation  of  matter. 

The  remarkable  connection  between  the  results  of  the  quanti- 
tative work  of  Faraday  and  the  chemical  equivalents  of  the  ele- 
ments, points  to  electrolysis  as  a  fertile  field  for  the  investigation 
of  the  yet  unknown  nature  of  chemical  affinity. 

683.  Electroplating. — The  principles  of  electrolysis  are  made 
use  of  in  the  mechanic  arts.     Articles  made  of  baser  metals  are 
covered  over  with  a  thin  deposit  of  silver  or  gold  and  are  said  to- 


TTTCTTTT-TP-DOT 


440  ELECTRICITY     AND     MAGNETISM. 

have  been  electroplated.  The  articles  to  be  plated  are  suspended 
in  a  bath  from  a  metallic  rod,  which  is  in  electrical  communication 
•with  the  negative  pole  of  a  battery  or  dynamo  (Fig.  393).  The 

bath  consists  of  a  solution 
of  some  salt  of  the  metal 
which  is  to  be  deposited, 
e.g.,  silver  or  gold  cyanide. 
The  current  from  the  posi- 
tive pole  of  the  dynamo  en- 
ters the  solution  by  means 
of  an  electrode,  C,  made  of 
the  same  metal  as  that  which 
is  contained  in  the  salt. 
Upon  passing  a  current,  the 

salt  of  the  solution  is  decomposed — the  metal  depositing  on  the 
article  to  be  plated,  and  the  acid  combining  with  the  electrode  C 
to  form  new  salt,  thus  maintaining  the  concentration  of  the  solu- 
tion. The  articles  to  be  plated  must  be  thoroughly  scoured  and 
cleansed  before  immersion  in  the  bath.  The  character  of  the 
results  obtained  depends  much  upon  the  character  and  concen- 
tration of  the  baths  and  upon  the  magnitude  of  the  currents  and 
electro-motive  forces  employed.  Full  details  must  be  looked  for 
in  technical  books. 

684.  Electrotyping. — If  the  object  to  be  plated  consists  of 
un  impression,  in  wax  or  paper  pulp,  of  the  type  from  which  a 
page  is  printed,  the  impress'ion  having  been  coated  with  fine  plum- 
bago to  render  it  a  good  conductor,  copper  deposited  upon  it  may 
be  removed,  and  having  been  stiffened  by  melted  lead  (or  some 
alloy)  poured  over  its  under  surface,  it  may  be  used  in  the  print- 
ing-press instead    of   the  .type.     It  is  then   called  an   electrotype 
plate,  and  when  not  in  use  may  be  preserved  indefinitely  for  suc- 
ceeding editions,  while  the  t}Tpe  of  which  it  is  a  copy  can  be 
distributed  and  used  for  other  purposes. 

685.  Counter-Electromotive  Force. — If  a  current  be  sent 
through  a  solution  of  alkaline  zincate  by  means  of  two  copper 
electrodes,  zinc  will  be  deposited  on  one  electrode  and  the  other 
will  become  oxidized.     If  the  connections  with  the  source  of  elec- 
tricity be  now  removed  and  transferred  to  an  electric  bell,  the  bell 
will  ring.     The  bath  and  electrodes  have  been  transformed  into  a 
galvanic  cell.    The  current  which  it  gives  is  in  a  direction  opposite  to 
that  which  caused  the  decomposition  of  the  solution.     Its  E.  M.  F. 
is  about  0  79  volt,  and  is  opposed  to  the  original  E.  M.  F.     Had 
ihe  original  E.  M.  F.  been  less  than  this  amount,  no  plating  of  the 


STORAGE    BATTERIES.  441 

electrodes  could  have  occurred.  The  E.  M.  F.  developed  in  the- 
solution  is  termed  a  counter-electromotive  force.  It  occurs  in  nearly 
all  electrolytic  actions,  except  when  the  electrodes  are  of  the  same 
metal  as  that  which  is  being  deposited,  e.g.,  copper  in  copper 
sulphate. 

The  counter-electromotive  force  developed  in  the  electrolysis 
of  dilute  sulphuric  acid  is  about  1.47  volt.  Hence,  to  perform 
the  electrolysis,  more  than  one  Daniell's  cell  is  necessary. 

The  counter- electromotive  force  constitutes  the  polarization  of 
a  primary  battery  mentioned  in  Art.  634. 

686.  Storage  Batteries.— The  copper  electrodes  in  alkaline 
zincate  of  the  preceding  article  represent  a  very  simple  form  of 
storage  battery  or  electrical  accumulator.  Upon  sending  a  current 
through  it,  the  zinc  is  deposited  and  the  battery  is  said  to  be 
charged.  Some  of  the  electrical  energy  has  been  transformed  into 
chemical  energy.  The  electrodes  may  be  removed  from  the  solu- 
tion, packed  away,  and  then  be  brought  forward  in  the  future  and 
be  made  to  turn  back  their  energy  into  electricity.  The  elec- 
tricity proper  has  not  been  stored  away,  but  the  energy  repre- 
sented by  it. 

The  first  successful  storage  battery  was  constructed  by  Gaston 
Plante  in  1860.  His  electrodes  were  made  of  sheet-lead,  and  the 
electrolyte  was  dilute  sulphuric  acid.  In  order  to  expose  a  large 
surface  of  electrodes  he  made  them  of  large  sheets  which  he  coiled 
up  into  spirals,  as  shown  in  Fig.  394,  the  two  plates  being  insulated 
from  each  other  by  rubber  bands  between  the  spirals. 
The  object  of  the  large  surface  was  to  increase  the 
capacity  of  the  cell.  The  spiral  form  was  conducive 
to  a  small  internal  resistance.  Upon  the  passage  of  a 
current  the  acid  was  decomposed  and  hydrogen  re- 
duced one  electrode  to  bright  metallic  lead,  while 
oxygen  coated  the  other  with  peroxide  of  lead. 
These  two  conditions  of  the  electrodes  rendered 
them  capable  of  giving  an  electro-motive  force  of  two 
volts.  By  repeated  charging  in  alternate  directions 
the  surfaces  of  both  electrodes  were  rendered  spongy, 
thus  exposing  an  increased  surface  to  the  action  of 
the  ions  and  increasing  the  capacity  of  the  cell  accordingly.  This 
preliminary  alternate  charging  was  termed  by*  him  "formation"  of 
the  electrodes,  and  was  performed  at  the  expense  of  costly  currents. 

In  order  to  reduce  the  time  and  expense  of  formation,  Faure 
used  lead  plates  as  a  support  and  covered  them  with  a  paste 
made  of  powdered  oxide  of  lead  mixed  with  sulphuric  acid.  This, 
paste  he  kept  in  place  by  covering  the  sheets  with  felt.  When  the 


442 


ELECTRICITY    AND     MAGNETISE. 


FIG.  395. 


-charging  current  was  connected  the  oxide  on  one  plate  was  changed 
to  a  higher  oxide,  and  on  the  other  plate  transformed  into  metallic 
sponge.  This  idea  of  Faure  was  an  excellent  one,  and  is  at  the 
foundation  of  the  construction  of  all  the  commercial  lead  accu- 
mulators. The  percentage  of  energy  recovered  by  discharge  was 
greatly  increased.  His  method  of  keeping  the  paste  in  place  by 
felts  was,  however,  soon  abandoned,  because  fine  lead  needles  soon 
filled  up  the  interstices  of  the  felt,  and  thus  made  a  metallic  con- 
nection between  the  electrodes.  Holes  were  then  punched  in  the 
lead  plates  and  the  paste  pressed  into  them.  A  large  number  of 
the  patents  recently  issued  for  accumulators  refer  to,  methods  of 
making  these  holes  and  pressing  in  the  paste,  or  to  the  shape  of  the 
holes  themselves  after  they  have  been  punched.  The  shapes  vary 
from  a  slight  depression  on  the  surface  to  a  hole  completely 
through  the  plate,  and  even  further,  to  a  hollow  plate,  with  small 

openings  leading  to  the  surface. 
A  great  deal  depends  upon  this 
shape,  for  the  paste  changes  its 
volume  during  the  process  of 
charging  and  discharging,  and  it 
would  tend  to  loosen  itself  from 
some  shaped  openings  and  fall 
to  the  bottom  of  the  cell,  while 
in  others  it  would  tend  to  tighten 
itself,  and  thus  provide  a  better 
contact. 

A  modern  commercial  stor- 
age battery  is  shown  in  Fig.  395. 
The  electrodes  are  made  up  of  a 
number  of  pasted  plates,  or  grids 
as  they  are  called.  The  grids  of 
-one  electrode  are  alternated  with  those  of  the  other,  and  are  all 

connected  by  luas  with  com- 

• '  i  .  i  FIG.  396. 

mon   cross-bars  which  consti- 
tute the  terminals  of  cell. 

687.  Capillary  Elec- 
trometer.— This  instrument 
is  for  the  measurement  of 
small  differences  ofr  potential 
not  exceeding  1  volt.  A  simple 
form  is  represented  in  Fig. 
396.  It  consists  of  two  up- 
right test-tubes  connected  by  a  horizontal  capillary  glass  tube  of 
about  mm.  internal  diameter. 


LIGHT    AND     ELECTRICITY.  443 

Into  one  of  the  test-tubes  is  poured  mercury  and  into  the  other 
ililute  sulphuric  acid.  The  heights  of  the  two  liquids  are  so  arranged 
that  the  dividing  surface  between  them  shall  be  in  the  horizontal  tube. 
Upon  subjecting  the  two  liquids  to  an  electro-motive  force,  applied 
at  two  platinum  terminals  fused  into  the  bottoms  of  the  test-tubes, 
an  electrolytic  action  will  be  started  at  the  point  of  the  capillary 
tube  where  the  acid  meets  the  mercury.  The  surface  tension  will 
be  accordingly  modified  and  the  balance  between  the  two  columns 
will  be  destroyed.  To  reproduce  a  balance  the  dividing  surface 
must  move  along  the  capillary  tube  in  one  direction  or  the  other, 
depending  upon  which  liquid  has  the  higher  potential.  The  dis- 
tance moved  depends  upon  the  potential  difference  and  becomes 
.a  measure  of  it. 

688.  Light  and  Electricity. — At  the  present  time  many  in- 
vestigators are  experimenting  upon  the  close  relation  between  the 
phenomena  of  light  and  those  of  electricity.     Trustworthy  results 
point  to  the  fact  that  electricity  is  the  lurniniferous  ether  itself,  as 
was  previously  stated.     A  motion  of  the  ether  is  unrestrained  in  a 
perfect  electrical  conductor.     In  a  dielectric  only  a  limited  dis- 
placement of  the  ether  particles  is  possible,  except  in  case  the 
dielectric  is  ruptured.     A  displacement  always  subjects  the  enclos- 
ing dielectric  to  a  strain,  and  can  be  produced  by  a  neighboring 
conductor  having  an  electrostatic  charge  or  by  its  conveying  an 
electrical  current.     The  displacement  resulting  from  a  current  is 
in  a  direction  opposite  to  the  current,  and  occurs  through  all  the 
dielectric  which  surrounds  the  current.     Upon  starting  the  current 
the.  displacements  near  the  conductor  occur  before  those  at  a  dis- 
tance.    The  velocity  of  propagation  of  the  first  impulse  causing 
displacement  is  the  same  as  the  velocity  of  light. 

A  full  exposition  of  the  ether  hypothesis,  and  to  what  extent 
it  explains  electrical  phenomena  is,  of  course,  out  of  place  here. 

689.  Double    Refraction   from    Electrostatic   Strain.— 
Kerr  showed  that  the  strain  in  a  dielectric,  caused  by  electrostatic 
difference  of  potential,  could  be  detected  by  means  of  polarized 
light.      He  placed  a  block  of  glass  between  two  Nicol's  prisms 
which  served  as  analyzer  and  polarizer.     Into  opposite  sides  of  the 
glass  were  bored  two  holes,  not  quite  meeting  each  other,  but  sep- 
arated by  about  2  mm.     Into  these  holes  were  placed  wires,  which 
were  connected  with  the  poles  of  a  Holtz  machine.     Upon  creating 
n  difference  of  potential  between  the  ends  of  the  wires  the  glass 
was  subjected  to  strain  and  exhibited  to  an  eye  placed  at  the  an- 
alyzing Nicol  similar  colors  to  those  given  by  mechanically  strained 
glass.     The  glass  was  made  doubly  refracting. 


444:  ELECTRICITY     AND    MAGNETISM. 

690.  Magneto-Optic  Twisting  of  the  Plane  of  Polarized 
Light. — Faraday  discovered  that  the  plane  of  polarization  of  a  ray 
of  light  which  traversed  a  magnetic  field  in  a  direction  parallel  to 
the  lines  of  force  was  twisted  by  the  field.     One  form  of  Faraday's 
experiment  is  to  place  a  straight  electro-magnet  between  two  Nic- 
ol's  prisms,  which  have  been  crossed  so  as  to  produce  extinction  of 
light.     Substitute  for  the  iron  core  of  the  magnet  a  tube  with 
glass  ends,  which  is  filled  with  bisulphide  of  carbon.     Before  the 
magnet  is  excited  a  ray  of  light  from  the  polarizer  passes  through 
the  liquid  and  is  brought  to  extinction  by  the  analyzer.     If,  now, 
the  magnet  be  excited  by  an  electrical  current,  the  analyzer  no 
longer  extinguishes  the  ray,  and  that  it  may  do  so  must  be  rotated 
through  a  certain  angle.     The  plane  of  the  ray  has  been  twisted 
or  rotated  by  the  magnetic  field.     The  direction  of  the  rotation  is 
the  same  as  the  direction  of  the  exciting  current.     By  reversing 
the  current  the  plane  will  be  twisted  in  an  opposite  direction.   The 
amount  of  the  rotation  of  the  analyzer  necessary  to  reproduce  ex- 
tinction of  the  ray  is  directly  proportional  to  the  length  of  the 
tube  and  to  the  strength  of  the  magnetic  field,  i.e.,  to  the  strength 
of  the  exciting  current.     It  also  depends  upon  the  nature  of  the 
liquid  in  the  tube.     In  general  it  may  be  said  that  substances  of 
high  refractive  indices  have  large  rotatory  powers. 

As  might  be  expected,  rays  of  the  different  colors  are  rotated 
through  different  angles.  Hence,  if  complete  extinction  by  large 
rotations  be  desired,  monochromatic  light  should  be  used. 

691.  Rotation  of  the  Plane  by  Reflection. — Kerr  discov- 
ered that  the  plane  of  polarization  was  rotated  when  the  ray  was 
reflected  from  the  polished  pole  of  the  iron  core  of  an  electro-mag- 
net.    In  this  case  the  direction  of  rotation  was  contrary  to  the 
direction  of  the  magnetizing  currents. 

692.  Photo-Electric  Properties  of  Selenium. — Selenium, 
when  thoroughly  annealed,  offers  a  resistance  to  an  electric  current 
which  is  dependent  upon  the  degree  to  which  it  is  illuminated. 
An  increase  of  illumination  decreases  the  resistance.     A  piece  of 
selenium,  whose  resistance  in  the  dark  was  500  ohms,  has  been 
known  to  decrease  its  resistance  to  50  ohms  upon  exposure  to 
bright  sunlight. 

This  peculiarity  of  selenium  is  made  use  of  by  Bell  in  the 
construction  of  his  photophone.  This  instrument  is  intended  for 
transmitting  sounds  to  a  distance  by  means  of  rays  of  light,  which 
are  reflected  from  a  mirror  that  is  made  to  vibrate  by  the  sounds. 
Light  of  varying  intensity  is  made  thus  to  impinge  upon  a  piece  of 
selenium,  which  is  connected  in  circuit  with  a  battery  and  a  Bell 


POWER    OF    ELECTRICAL    CURRENTS.  445 

telephone  receiver.  The  variations  in  the  resistance  of  the  selen- 
ium, because  of  the  varied  illumination,  cause  variations  of  the  cur- 
rent in  the  receiver,  which  serve  to  reproduce  the  sounds. 

Quite  recently  Shelford-Bidwell  has  exhibited  an  apparatus  in 
which  selenium  is  made  to  light  the  gas  as  darkness  comes  on  and 
to  turn  it  off  as  daylight  appears. 

Problems. 

1.  How  much  copper  will  be  deposited   by   a   current  of   3 
amperes  in  an  hour  ? 

2.  A  current  of  0.5  ampere  is  used  for  preparing  pure  silver 
by  electrolysis  :  how  long  must  the  current  be  allowed  to  flow  in 
order  to  obtain  a  deposit  of  4  grams  ? 

3.  What  is  the  strength  of  a  current  which  deposits  a  milli- 
gram of  copper  per  minute  ? 

4.  It  is  found  that  a  current  of  1.868  ampere  deposits  1.108 
gram  of  copper  in  half  an  hour  :  what  value  does  this  give  for  the 
electro-chemical  equivalent  of  copper  ? 

5.  What  is  the  strength  of  a  current  which  deposits  0.935  gram 
of  copper  in  1  hour  and  10  minutes. 


CHAPTEK    X. 

THE  RELATIONS  BETWEEN  ELECTRICITY  AND  HEAT, 

693.  Power  of  the  Electrical  Current.  —  A  current  whose 
strength  is  c  carries  in  t  seconds  c  t  units  of  electricity  from  a 
potential  Fto  one  of  V.  The  work  which  has  to  be  expended  in 
doing  this  is  c  t  (V  —  F),  as  was  shown  in  Art.  567.  In  this  case 
V  —  F  is  equal  to  the  electro-motive  force  E,  which  is  sending  the 
current.  Hence,  representing  the  work  by  A,  we  have 

A  —  c  t  E. 

If  c,  t,  and  E  are  measured  in  absolute  units,  the  work  is  given  in 
ergs. 

The  power  of  the  current  P  being  the  rate  at  which  the  work 
is  done,  i.e.,  the  work  divided  by  the  time  required  to  perform  it 
is  expressed  by  the  formula 


Expressing  c  and  E  in  amperes  and  volts  respectively  will  di- 


446  ELECTRICITY    AND    MAGNETISM. 

vide  the  ergs  per  second  by  107.     This  gives  the  power  in  watts 
(Art.  38). 

E 
Inasmuch  as  c  =  —  and  E  =  c  R,  by  Ohm's  law,  these  values 

may  be  substituted,  and  we  have,  further, 


P  =  c3  R. 

694.  Heat   Developed  in  a  Conductor.  —  Whenever  the 
energy  which  is  represented   by  a  current  is  not  expended   in 
doing  external  work,  as  in  driving  motors  or  decomposing  electro- 
lytes, it  is  transformed  into  heat.     The  conductor  which  carries 
the  current  becomes  heated.     If  a  conductor  of  resistance,  E,  car- 
ries a  current  c,  then,  by  Ohm's  law,  the  difference  of  potential 
between  its  ends,  E  =  c  E.     The  energy  represented  by  the  cur- 
rent is,  as  in  the  preceding  article, 

A  —  c  I  .E  =  c2  E  t  ergs. 

This  energy  is  transformed  into  heat.  To  express  the  heat  in 
gram-calories,  Joule's  mechanical  equivalent  of  heat  must  be  intro- 
duced. Without  going  through  with  the  transformations  it  is 
sufficient  to  say  that  a  current  of  c  amperes  flowing  for  t  seconds 
through  E  ohms  communicates  to  the  conductor  carrying  it 
H  —  c2  E  t  0.24  gram-calories. 

695.  Rise  in  Temperature  of  the  Conductor.  —  A  long 
thick  wire  could  have  the  same  resistance  as  a  short  thin  one,  but 
a  given  current  traversing  them  for  a  given  time  would  produce 
the  same  quantities  of  heat  in  each.     The   short  thin  wire,   not 
weighing  so  much,  might  have  its  temperature  raised  several  hun- 
dred degrees,  while  the  thick  wire  would  suffer  a  rise  of  a  few  de- 
grees only. 

In  order  to  determine  what  rise  in  temperature  will  accompany 
ra  given  quantity  of  heat  imparted,  account  must  be  taken  of  the 
(dimensions  of  the  conductor,  the  specific  heat  of  the  substance  of 
-which  the  conductor  is  composed,  and  the  temperature  coefficient 
of  the  conductor,  i.e.,  the  amount  by  which  its  resistance  would  in- 
crease under  a  rise  of  one  degree  of  temperature.  A  full  considera- 
tion cannot  be  considered  in  these  chapters.  It  is  well  to  know, 
however,  that,  in  different  wires  of  the  same  material,  traversed  by  the 
same  current,  the  rise  in  temperature  is  inversely  proportional  to  the 
fourth  power  rf  their  diameters. 

A  wire  of  given  resistance,  traversed  by  a  given  constant  current, 
will  receive  the  same  amount  of  heat  each  second  that  the  current 
flows.  After  a  short  time  the  temperature  of  the  wire  may  rise  to 


c       . 

UNIVERSITY) 

V^  '   OF  J 

HOT    WIRE    AMMETERS.  44.7 


»uch  a  point  that  it  gives  off  to  surrounding  objects,  by  radiation 
and  conduction,  just  as  much  heat  as  it  receives  in  every  second. 
The  temperature  then  remains  constant  at  this  point  as  long  as 
the  flow  is  maintained. 

The  heat  effects  mentioned  may  be  illustrated  by  sending  a 
strong  current  through  a  chain,  whose  alternate  links  are  made  of 
platinum  and  silver  wire.  The  platinum  links  will  be  heated  to 
luminosity  while  the  appearance  of  the  silver  remains  unaltered. 
The  reason  for  this  is  that  the  platinum  offers  a  much  greater  re- 
sistance than  the  silver,  and  its  specific  heat  is  less. 

Platinum  wires,  heated  red-hot  by  currents,  are  much  used  by 
surgeons  for  cauterization.  They  are  much  easier  of  manipulation 
than  the  knife. 

696.  Hot  Wire  Ammeters  and  Voltmeters. — The  expan- 
sion in  length  which  a  wire  undergoes  when  its  temperature  is 
raised  to  a  certain  point  by  a  current  which  traverses  it,  can  be  made 
a  measure  of  the  strength  of  the  current*  A  given  wire  has  a 
definite  length  at  a  given  temperature.  Increasing  the  tempera- 
ture increases  the  length.  Every  current  produces  a  definite  length 
in  the  wire.  Different  current  strengths  correspond  to  different 
lengths.  A  measurement  of  the  length  can  thus  be  made  a  meas- 
ure of  the  current  strength. 

A  simple  ammeter,  whose  action  depends  upon  this  principle,  is 
represented  in  Fig.  397.  The  current  to  be  measured  is  passed 

FIG.  397. 


through  a  long  and  thin  platinum  or  iron  wire,  one  of  whose  ends 
is  clamped  in  a  stationary  binding-post.  The  other  end  passes 
around  and  is  fastened  to  a  small  metallic  cylinder.  This  cylinder 
turns  upon  a  metallic  pivot  fastened  in  another  binding-post. 
The  current  having  traversed  the  wire  leaves  it  by  this  binding-post. 
The  wire  is  subjected  to  a  constant  strain,  exerted  by  a  spiral  spring 
attached  to  the  periphery  of  a  disc,  which  is  fastened  to  one  end 
of  the  cylinder.  The  disc  carries  a  radial  pointer,  whose  end 
moves  over  a  graduated  scale  whenever  the  length  of  the  wire  is 
ohanged  by  a  change  in  temperature  caused  by  a  current.  The 


448  ELECTRICITY    AND    MAGNETISM. 

graduation  of  the  scale  is  empirical,  being  determined  by  the  assist- 
ance of  some  other  current  measurer. 

As  the  current  strength  is  dependent  upon  the  difference  of  po- 
tential between  the  two  binding-posts,  it  is  evident  that  the  instru- 
ment may  be  graduated  as  ^voltmeter,  i.e.,  will  indicate  the  volts  im- 
pressed upon  it.  As  it  is  not  desirable  that  a  large  current  should 
flow  through  a  voltmeter,  the  wire  of  such  an  instrument  should  have 
a  large  resistance.  The  voltmeters  of  Cardew  are  constructed  on 
this  principle.  Sometimes  a  high  resistance  coil  is  inserted  in 
series  with  the  wire,  and  then  the  voltmeter  readings  indicate  the 
fall  in  potential  between  the  terminals  of  the  spool  and  wire  in 
series. 

Hot  wire  ammeters  and  voltmeters  can  be  employed  to  meas- 
ure currents  and  voltages  which  rapidly  alternate  their  directions. 
For  the  heat  produced  being  dependent  on  the  square  of  the  cur- 
rent strength  is  positive,  whether  the  current  flows  in  a  positive  or 
negative  direction. 

697.  Electric  Welding.  —  The  welding  together  of  two 
pieces  of  metal,  by  means  of  the  electric  current,  as  done  in  the 

Thomson  process,  depends  upon  the  heat 
produced.  The  pieces  are  pressed  to- 
gether and  a  powerful  current  (some- 
times 50,000  amperes)  is  sent  across  the 
juncture.  The  consequent  heat  renders 
the  metal  plastic,  and  upon  cooling  a 
most  perfect  joint  is  obtained. 

698.  The  Electric  Arc. — If  two 
rods  of  carbon,  traversed  by  a  current 
from  a  source  of  at  least  40  volts  electro- 
motive force,  be  touched  together  at  their 
ends  and  then  be  separated  by  a  few 
millimeters'  distance,  an  electric  flame  or 
arc  will  be  observed  to  pass  over  this  dis- 
tance. A  brilliant  light  will  accompany 
it,  the  extreme  brilliancy  being  at  the 
end  surfaces  of  the  rods.  If  allowed  to 
burn  for  a  few  moments  the  rods  and 
flame  will  present  an  appearance  like  that 
represented  in  Fig.  398.  The  end  of  the 
positive  rod  will  have  formed  itself  into  a 
sort  of  crater,  while  the  end  of  the  neg- 
ative will  have  become  pointed.  If  al- 
lowed to  burn  for  some  time,  the  rods  will  be  consumed,  and,  in  a. 


THERMO-ELECTRICITY.  449 

•given  time,  about  twice  as  much  of  the  positive  rod  will  be  con- 
.sumed  as  of  the  negative. 

In  order  to  form  an  arc  it  is  necessary  that  the  points  be  at 
first  in  contact.  When  in  loose  contact  the  current  encounters  a 
great  resistance,  and  accordingly  heats  the  points  until  a  tempera- 
ture is  reached  which  is  sufficient  to  vaporize  the  carbon.  Carbon 
vapor  is  a  much  better  conductor  of  electricity  than  air,  and 
whereas  an  arc  could  not  be  maintained  across  an  air  space,  yet  it 
can  be  across  a  space  filled  with  this  vapor. 

The  heat  at  the  vapor  portion  of  the  arc  is  intense,  being  suffi- 
cient to  vaporize  the  most  refractory  substances,  of  which  carbon 
itself  is  the  best  example.  The  heat  at  the  crater,  though  not  so 
intense,  is  the  cause  of  greater  illumination,  because  of  being  asso- 
ciated with  a  solid  instead  of  a  vapor. 

Recent  investigations,  concerning  the  fall  of  potential  uloug  the 
arc,  indicate  that  a  large  portion  of  the  electrical  energy  repre- 
sented by  it  is  consumed  in  maintaining  the  heat  of  the  crater. 

699.  Incandescent   Electric    Lamps.  —  These    lamps   con- 
sist of  filaments  of  carbonized  bamboo,   paper,   or  silk,   which  are 
heated  to  incandescence  by  the  current.     That  the  filaments  may 
not  be  consumed  by  combustion,  they  are  sealed  into  glass  bulbs, 
from  which  the  air  has  been   exhausted.     Although  no  oxygen  is 
present,  the  filaments  become  disintegrated  by    continuous   use. 
Particles  of  carbon  escape  from  the  surface  of  the  filament  and  are 
oftentimes  deposited  upon  the  interior  of  the   bulb,    causing    a 
brownish  opalescent  appearance. 

700.  Thermo-Electricity.  —  Let  two  bars  of  bismuth  (6)  and 
antimony  (a)   be   soldered  together  as  in   Fig.   399.     If,  now,  the 
joint  S  be   heated  by  a 

lamp  a  current  will  flow  FlG-  '^®- 

across  the    heated   June-  s 

tion  from  the  bismuth  to      .     ^  *     - 
the  antimony,  as  will  be        "* 


shown    by    the    galvano- 
meter G. 

The  electro-motive  force  of  the  current  depends  upon  the  metals 
in  contact  at  the  heated  junction.  If  any  one  of  the  metals  given 
below  be  joined  with  any  one  following  it  in  the  list,  upon  apply- 
ing heat  the  current  will  flow  across  the  junction  from  the  former 
to  the  latter  :  Bismuth,  lead,  platinum,  tin,  zinc,  copper,  iron,  an- 
timony. 

The  thermo-electro-motive  force  is  proportional  to  the  difference  of 
temperature  between  the  junction  and  the  rest  of  the  circuit. 


450 


ELECTRICITY    AND    MAGNETISM. 


The  E.  M.  F.  of  a  single  thermoelement  is  very  small.  If  the- 
junction  of  a  copper-iron  element  be  heated  1°  C.  above  the  tem- 
perature of  the  rest  of  the  circuit,  the  E.  M.  F.  developed  is  about 
fourteen  millionths  of  a  volt. 

In  some  cases,  e.g.,  with  iron,  a  continued  increase  of  tempera- 
ture at  the  junction  finally  reverses  the  direction  of  the  current. 

701.  Thermo-Electric  Pile. — If  a  series  of  bars  of  bismuth 
and   antimony  be   arranged,   as   in   Fig.  400,   and   the   junctions 

marked  3  and  4  be  equally  heated, 
no  current  will  be  indicated  by  the 
galvanometer ;  for  the  flow  at  3 
would  be  from  the  bismuth  to  the 
antimony  as  indicated  by  the  arrow, 
while  at  4  it  would  also  be  from  b 
to  a,  as  shown,  and  these  two  cur- 
rents would  neutralize  each  other. 
But  if  we  heat  only  one  set  of  junctions,  the  odd-numbered  for 
instance,  then  a  current  flows  whose  electro-motive  force  is  pro- 
portional to  the  number  of  heated  junctions. 

A  set  of  twenty  or  thirty  pairs,  conveniently  arranged  so  that 
the  alternate  junctions  may  be  simultaneously  subjected  to  heating- 
or  cooling  effects,  is  called  a  thermo-pile,  and  has  been  an  impor- 
tant instrument  in  investigations  upon  radiant  heat. 

702.  Peltier  Effect. — Peltier  discovered  a  phenomenon  which 
is  the  converse  of  that  mentioned  in  the  preceding  articles.     He 
found  that,  if  a  current  of  electricity  be  sent  through  a  junction  of 
dissimilar  metals,  the  junction  becomes  heated  or  cooled  according 
to  the  direction  of  the  current.     For  instance,  if  a  current  be  sent 
through  a  junction   from  bismuth  to  antimony,  the  junction  will 
absorb  heat,  i.e.,  become  cooled.     If  the  current  be  reversed   the 
junction  will  become  heated. 

The  heat  thus  produced  is  not  owing  to  the  resistance  of  tbe 
conductors.  For  the  heat  from  resistance  is  not  altered  by  a 
change  in  the  direction  of  the  flow  of  the  current.  Cooling  can 
never  result  from  ohmic  resistance.  Again,  the  heat  of  the  Peltier 
effect  is  proportional  to  the  current  strength  simply,  whereas  the 
heat  from  resistance  is  proportional  to  the  square  of  the  current 
strength. 

Problems. 

1.  An  11,000  watt  dynamo  develops  an  E.  M.  F.  of  110  volts : 
(a)  What  is  the  current  strength  in  the  mains  ?  (b)  How  many  in- 
candescent lamps,  of  220  ohms  hot  resistance,  will  it  light,  provid- 


THE    ELECTRICAL    UNITS.  451 

ing  they  are  arranged  in  multiple  arc?  (c)  How  many  gram-calo- 
ries will  be  developed  in  each  lamp  per  second  ?  (d)  How  many 
watts  will  be  consumed  by  each  lamp?  [  (a)  100  amperes. 

A         \  (b)  200  lamps. 
m'   }  (c)  13.2  calories. 
L  (d)  55  watts. 

2.  How  much  power  is  required  to  properly  operate  an  arc 
lamp  which  carries  10  amperes  and  has  a  difference  of  potential  of 
45.2  volts  between  its  terminals  ? 

3.  How  many  calories  are   developed  per  minute  in  a  wire  of 
100  ohms  resistance,  traversed  by  5  amperes  ? 

4.  A  wire  of  2  ohms  resistance  placed  in  100  grams  of  water  is 
traversed  by  a  certain   current,  which,  in  20  minutes,  raises  the 
temperature  of  the  water  from  18°  to  28°  C.:  what  is  the  current 
strength  ?  Ans.  1.32  amperes,  nearly. 

The  Electrical  Units. 

Electrical  magnitudes  may  be  expressed  in  three  different  sets 
of  units.  Two  of  them — the  absolute  electrostatic  and  the  absolute 
electro-magnetic  units — are  termed  absolute  because  they  are  units 
derived  from  the  absolute  units  (Art.  4)  of  length,  mass,  and  time, 
viz.,  the  centimetre,  gram,  and  second.  The  third  set  are  called 
practical  units,  because  they  are  the  ones  which  are  employed  by 
practical  electricians.  They  are  either  decimal  multiples  or  deci- 
mal parts  of  the  electro-magnetic  units. 

ELECTROSTATIC  UNITS. 

The  Unit  of  Quantity  of  electricity  is  that  quantity  which,  when 
placed  at  a  distance  of  one  centimetre  from  a  similar  and  equal 
quantity,  repels  it  with  a  force  of  one  dyne  (Art.  563). 

The  Unit  Strength  of  Current  flows  in  a  circuit  when  a  unit 
quantity  of  electricity  passes  any  section  of  the  conductor  in  one 
second. 

The  Unit  Difference  of  Potential  exists  between  two  points 
when  it  requires  an  expenditure  of  one  erg  of  work  to  bring  a 
unit  quantity  of  electricity  from  one  point  to  the  other  against  the 
electric  force. 

The  Unit  of  Resistance  is  offered  by  that  conductor  which,  when 
interposed  between  two  bodies  whose  potentials  are  maintained  at  a 
constant  difference  of  unity,  allows  a  unit  current  to  pass  along  it. 

The  Unit  of  Capacity  is  possessed  by  that  conductor  which 
requires  that  it  be  charged  with  a  unit  quantity  of  electricity  in 
order  that  its  potential  may  be  raised  from  zero  to  unity. 

ELECTRO-MAGNETIC  UNITS. 
The  Unit  Strength  of  Current  is  such  that,  when  flowing  through 


452  ELECTRICITY    AND    MAGNETISM. 

a  conductor  of  one  centimetre  length  which  is  bent  into  an  arc  of 
one  centimetre  radius,  it  will  exert  a  force  of  one  dyne  on  a  unit 
magnetic  pole  situated  at  the  centre. 

The  Unit  Quantity  of  electricity  passes  in  one  second  through  a  sec- 
tion of  a  conductor  which  is  traversed  by  a  current  of  unit  strength. 

The  Unit  Difference  of  Potential  (or  of  Electro-motive  Force)  exists 
between  two  points  when  it  requires  the  expenditure  of  one  erg  of 
work  to  bring  a  unit  of  electricity  from  one  point  to  the  other 
against  the  electric  force. 

The  Unit  of  Resistance  is  offered  by  that  conductor  which,  when 
interposed  between  two  bodies  whose  potentials  are  maintained  at 
a  constant  difference  of  unity,  allows  a  unit  current  to  pass  along  it. 

The  Unit  of  Capacity  is  possessed  by  that  conductor  which 
requires  that  it  be  charged  with  a  unit  quantity  of  electricity  in 
order  that  its  potential  may  be  raised  from  zero  to  unity. 

A  little  consideration  will  show  that  in  the  electrostatic  and 
electro-magnetic  systems  the  definitions  of  all  the  units  except  that 
for  quantity  are  identical.  Whereas  the  electrostatic  unit  of  quantity 
is  determined  from  its  exerting  a  dyne  of  force  on  another  unit 
quantity,  the  electro-magnetic  unit  of  quantity  is  determined  from 
its  exerting  a  dyne  of  force,  when  moving  as  a  current,  on  a  unit 
magnetic  pole.  The  electro-magnetic  unit  is  about  3  x  10'°  times 
the  electrostatic  unit.  This  numerical  factor  is  the  same  as  the 
velocity  of  the  propagation  of  light  expressed  in  centimetres  per 
second.  This  fact,  combined  with  certain  mathematical  relations 
which  exist  between  the  two  units,  is  of  great  significance  in  sus- 
taining the  ether  theory  of  electricity. 

PRACTICAL  UNITS. 

Many  of  the  absolute  units  would  be  inconveniently  large  and 
others  would  be  inconveniently  small  for  practical  use.  Therefore 
the  following  units,  based  upon  the  electro-magnetic  units,  are  used  : 

Electromotive  force Volt         =  108    electro-magnetic  units. 

Resistance Ohm        =  109  "  " 

Current Ampere  =  10  ~l  "  «' 

Quantity Coulomb  =  10-'  "  " 

Capacity Farad     =  10- 9  "  " 

Even  these  units  are  not  of  a  magnitude  suited  for  the  use  of  all 
electricians.  Thus  a  physician  uses  currents  whose  strengths  can 
be  more  easily  expressed  in  thousandths  of  an  ampere.  The  prefix 
milli-  is  therefore  used  for  "one  thousandth  "  and  a  milliampere  is 
the  thousandth  part  of  one  ampere.  Capacities  are  best  expressed 
in  millionths  of  a  farad  or  microfarads.  The  high  resistances 
offered  by  insulations  are  conveniently  expressed  in  megohms  = 
one  million  ohms. 


A  COURSE  IN  ELECTRICAL 
MEASUREMENTS. 


INTKODUCTOKY. 

To  the  Instructor. — The  student  who  carries  out  the  exper- 
iments outlined  in  the  following  course  will  become  acquainted 
with  methods  generally  employed  in  determining  electrical  mag- 
nitudes. The  accuracy  of  the  results  which  he  may  obtain  is 
largely  limited  by  the  care  exercised  in  eliminating  disturbing 
conditions,  and  to  a  certain  extent  by  the  character  of  the  appa- 
ratus employed.  It  is  possible,  however,  to  make  very  accurate 
measurements  with  quite  ordinary  apparatus.  A  laboratory  should 
possess  a  standard  resistance  coil,  a  standard  thermometer,  and 
a  set  of  standard  weights.  A  cheap  rheostat,  if  wound  with  wire 
of  negligable  or  known  temperature  coefficient  and  of  small  ther- 
mo-electric power  (e.g.,  manganin),  can  be  calibrated  with  the  aid 
of  the  standard  resistance  and  be  made  to  yield  accurate  results. 
Standard  Weston  voltmeters  and  ammeters  are  great  conveniences. 
The  cheap  D'Arsonval  galvanometers  sold  by  Queen  &  Co.  may, 
however,  be  used  both  as  ammeters  and  as  voltmeters.  Observa- 
tions should  be  made  by  means  of  a  telescope  and  scale.  Tele- 
scopes which  are  entirely  satisfactory  may  be  made  from  ordinary 
spectacle  lenses.  If  the  telescope  be  kept  at  a  fixed  distance  from 
the  mirror  of  the  galvanometer,  a  suitably  sized  copper  wire 
shunted  between  the  galvanometer  terminals  will  reduce  it  to  a 
direct  reading  ammeter  independent  of  temperature  variations, 
but  liable  to  slow  alterations,  owing  to  decrease  in  strength  of 
the  magnets  with  the  time.  A  high  resistance  of  proper  magni- 
tude placed  in  series  with  the  galvanometer  transforms  it  into  a 
direct-reading  voltmeter.  High  resistances  of  any  magnitude 
(approximate)  may  be  purchased  from  the  Dixon  Crucible  Co.,  of 
Jersey  City,  for  a  few  cents.  They  are  of  graphite  and  in  form 
of  rods.  Their  ends  can  be  copper-plated  and  copper  wires  can 
be  soldered  to  the  plating.  Adjustments  can  be  made  by  scraping 


454  ELECTRICAL    MEASUREMENTS. 

away  a  portion  of  the  plating.  These  galvanometers,  if  of  high 
resistance  (1,000  ohms),  may  be  used  for  all  the  work  in  this 
course.  When  used  as  ballistic  galvanometers,  the  period  of  os- 
cillation is  rather  small,  and,  further,  it  must  be  constantly  borne 
in  mind  that  the  damping  is  dependent  on  the  resistance  of  the 
circuit.  Some  of  the  exercises  require  that  electricity  be  taken 
from  the  electric-lighting  street  circuit.  These  exercises  are  more 
conveniently  carried  out  in  this  manner,  but  may  be  performed 
with  the  assistance  of  batteries.  When  the  street  circuit  is  of 
constant  potential,  the  amount  of  current  employed  is  conven- 
iently regulated  by  means  of  altering  in  number  interposed  elec- 
tric lamps,  coupled  in  multiple  arc. 

To  the  Student. — Physical  laboratory  instruction,  to  be  of 
most  value  in  education,  should  develop  in  the  student : 

1.  A  habit  of  observation  of  the  phenomena  of  nature,  both 
ordinary  and  extraordinary. 

2.  The  ability  to  accurately  and  truthfully  record  these  obser- 
vations in  a  note-book. 

3.  The  ability  to  draw  correct  and  logical  inferences  from  the 
noted  observations,  and 

4.  The  ability  to  present  in  concise  and  perfect  English  the 
observations  and  the  results  to  be  inferred  from  them. 

In  general,  it  is  always  advisable  to  use  the  greatest  possible 
accuracy  of  observation  that  is  allowable  with  the  apparatus  em- 
ployed. In  some  cases,  however,  when  other  observations  of  less 
possible  accuracy  are  to  be  combined  in  forming  a  final  result, 
less  care  may  be  taken.  A  single  observation  is  no  security  against 
blunders.  A  number  of  observations  is,  however,  and,  in  addition, 
diminishes  the  probable  error  of  the  mean.  Errors  of  observation, 
and  all  errors  which  are  as  liable  to  be  above  as  below  the  true 
value,  can  be  diminished  in  this  manner  only.  Instrumental 
errors  can  sometimes  be  obviated  by  changing  in  each  observation 
the  conditions  of  the  experiment ;  for  example,  in  measuring  the 
length  of  an  object  by  means  of  a  scale,  an  error  of  the  graduation 
can  be  eliminated  by  placing  the  object  upon  different  portions 
of  the  scale.  A  large  number  of  observations  will  increase  the 
accuracy  of  results. 

In  recording  observations,  truthfulness  is  paramount.  Eecord 
as  an  observation  only  that  which  has  been  observed.  Several 
students  recorded  in  their  note-books  the  length  of  an  object  as 
observed  to  be  19  cms.  because  it  extended  from  the  0  to  the  19 
division  of  a  scale.  The  scale  had  no  division  at  17  and  was 
faulty.  The  length  of  the  object  was  18  cms.  The  students- 


COMPARISON    OF     RESISTANCES.  455 

should  have  noted  what  they  observed,  and  not  what  they  in- 
ferred. 

The  record  should  always  indicate  the  accuracy  of  an  observa- 
tion. If  an  ammeter  which  is  readable  to  the  hundredth  of  an 
ampere  should  indicate  a  current  of  exactly  2  amperes,  the  record 
should  be  2.00,  not  simply  2.  The  two  ciphers  in  the  decimal 
places,  although  of  no  numerical  value,  still  -indicate  the  accuracy 
of  the  observation,  and  to  what  extent  the  observation  may  be 
relied  upon. 

Perfect  freedom  in  the  matter  of  drawing  inferences  is  not  com- 
patible with  a  course  of  electrical  measurements.  Original  research. 
and  investigation  alone  give  this.  Yet  the  failure  of  many  experi- 
ments to  yield  reasonable  results  upon  first  trial  give  to  the  student 
the  opportunity  of  inferring  the  causes  of  the  failure,  and  it  is  ad- 
visable that  the  student  should  unassisted  determine  these  causes.. 

The  student  is  admonished  : 

1.  To  interfere  in  no  other  student's  experiments. 

2.  To  consider  neatness  and  cleanliness  as  essential  to  good 
work. 

3.  To  disconnect  all  apparatus  after  use. 

4.  To  arrange  and  adjust  all  apparatus  so  that  the  greatest 
accuracy  is  obtained  with  the  least  inconvenience  to  the  observer. 

RESISTANCES. 

Comparison  of  Resistances.  —  It  is  not  often  that  the  de- 
termination of  a  resistance  in  absolute  measure  is  required.  In 
nearly  all  cases  a  resistance  is  measured  only  in  so  far  as  its  ratio 
to  some  known  standard  resistance  is  determined.  Standard  re- 
sistances are  made  of  German  silver,  platinoid,  or  manganin  wire, 
and  are  wound  bifilar.  These  substances  are  chosen  because  of 
their  high  resistivity,  and  because  of  their  small  variation  in  re- 
sistance with  the  temperature.  If  the  resistance  of  a  conductor  at 
18°  C.  "be  .#,  then  its  resistance  at  any  near  temperature,  t,  may  be 
represented  by  the  formula 


where  a  is  the  temperature  coefficient 

For  German  silver  a  =  0.00024  to  0.0006. 

For  copper  a  =  0.004. 

For  carbon  a  =  -  0.0002  to  —  0.0007. 

For  electrolytes      a  =  —  0.014    to  -  0.030. 
Attention  is  called  to  the  fact  that  the  resistance  of  metals  in- 
creases with  a  rise  in  temperature,  while  the  resistance  of  carbort 
and  electrolytes  decreases. 


456  ELECTRICAL    MEASUREMENTS. 

Rheostats  or  resistance-boxes  are  stamped  with  a  normal  tem- 
perature. This  means  that,  at  the  given  temperature,  the  resist- 
ance of  all  the  coils  in  series  is  exactly  equal  to  their  nominal  value. 
The  individual  coils,  however,  may  none  of  them  have  the  exact 
resistance  with  which  it  is  stamped.  A  table  of  corrections  should 
accompany  each  box.  By  applying  the  correction  and  then  cor- 
recting for  temperature,  the  exact  resistance  of  any  coil  may  be 
obtained. 

E.g. :  The  correction  for  a  100-ohm  German  silver  coil  is  + 
0.12  at  the  normal  temperature  18.8°,  and  the  temperature  coeffi- 
cient is  0.00035.  At  21.8°  the  resistance 

=  100.12[1  +  (21.8  -  18.8)0.00035]  =  100.23  ohms. 

Care  must  be  taken  that  the  resistance  of  a  connecting  wire  be 
not,  through  oversight,  added  to  a  resistance  to  be  compared  or 
to  a  standard.  If  it  must  of  necessity  be  added,  its  value  should 
be  added  or  its  influence  considered.  Bad  contacts  often  add  re- 
sistance in  unsuspected  places.  The  ends  of  connecting  wires 
should  be  scraped  and  fastened  firmly  in  the  binding  posts.  The 
plugs  of  a  rheostat  should  be  twisted  in  their  respective  holes. 

Method  of  Substitution — Two  resistances  are  equal  to  each 
other  if,  when  one  replaces  the  other  in  a  given  circuit,  the  current 
strength  remains  unaltered. 

Apparatus. — Daniell  cell,  galvanometer,  rheostat,  and  x. 

Directions. — Form  a  circuit  of  cell,  galvanometer,  and  x.  Note 
deflection  0.  Substitute  for  x  such  a  resistance  El  as  to  yield  a 
deflection  Ol  slightly  less  than  0.  Then  substitute  E^  so  as  to  yield 
02  slightly  larger  than  0.  Then 


Prove  formula.     Why  is  a  Daniell  cell  used  ? 

What  accuracy  have  you  attained  ? 

This  method  is  used  in  determining  insulation  resistances, 
•which  are  very  large. 

For  measuring  small  resistances  the  galvanometer  resistance 
should  be  small.  Why? 

Direct  Method  (Ohm).  —  I.  Apparatus. — Mirror  galva- 
nometer (shunted),  Daniell  cell,  rheostat,  and  x. 

Directions. — Form  a  circuit  of  cell,  connecting  wires,  and  gal- 
vanometer. Observe  small  deflection  6,  which  is  proportional  to 
the  current  C.  Insert  x  in  circuit  and  observe  Ox,  i.e.,  Cx.  Sub- 


PROJECTION    OF     POTENTIALS.  457 

stitute  for  x  a  known  resistance  R  and  observe  02,  i.e.,  C3.     Then 


- 


-c\    cx 


-e    ex 


Evidently  this  method  is  good  for  measuring  resistances  while 
a  current  is  traversing  them.  What  difference  would  this  make 
in  the  case  of  incandescent  lamps  ?  An  ammeter  may  be  used  in- 
stead of  a  galvanometer  and  the  currents  be  read  off  directly. 

Prove  the  correctness  of  the  formula. 

II.  Apparatus.  —  Voltmeter,  ammeter,  constant  voltage,  and  x. 

Directions.  —  Form  a  circuit  as  indicated  in  Fig.   401.      Ob- 
serve the  amperes  C  in  the  ammeter  A 
and  the  volts   E  in   the  voltmeter  V. 
Let  the  resistance  of  the  voltmeter  be 
E.      Then 

E 


FlG-  401- 


x  = 


•-J 


Determine  the  probable  error  in  your  results. 

III.  Apparatus. — Same  as  in  II. 

Directions. — Form  circuit  as   indi-  FlQ-  402- 

cated  in  Fig.  402.  Observe  amperes  G 
in  A  and  the  volts  E  in  V.  Let  R  =  re- 
sistance of  ammeter.  Then 


t 


Projection  of  Potentials.  —  Apparatus.  —  High-resistance 
sensitive  galvanometer,  a  known  resistance  R,  constant  source  of 
E.  M.  F.,  and  x. 

Directions.  —  Form  a  circuit  of  E.  M.  F.  R,  and  x.  From  the 
extremities  of  x  lead  off  to  galvanometer.  Note  the  deflection  0. 
Transfer  the  galvanometer  connections  to  the  extremities  of  R. 
Note  the  deflection  9l  [R  should  be  so  chosen  in  respect  to  x 
that  0  and  Ol  shall  be  nearly  equal].  Then 


This  method  is  most  often  employed  for  comparing  small  resist- 
ances. Before  making  this  measurement  draw  a  diagram  of  the 
connections. 

Resistivity.  —  The  resistivity  of  a  substance  is  the  resistance 
which  a  cube  of  the  substance,  with  faces  of  a  sq.  cm.  would  offer 


UNIVERSITY 


458 


ELECTRICAL    MEASUREMENTS. 


•to  a  current  entering  one  face  and  flowing  out  of  the  opposite  face. 
Hence  the  resistance  of  a  wire,  made  of  a  substance  of  resistivity 
/>,  whose  length  is  I  cms.  and  whose  diameter  is  d  cms.  is 

4J 


P  = 


The  resistance  may  be  measured  by  the  projection  of  potentials, 
I  by  means  of  a  cm.  scale,  and  d  by  means  of  a  micrometer  screw. 

TABLE  or  RESISTIVITIES. 

Substance.  Resistivity  at  0°  C. 

Silver  (annealed) 1.504    x     1Q-6 

Copper  (soft) 1.594 

Aluminum 2.912 

Platinum 9.057 

Iron 9.716 

German  silver 20.93 

Mercury .94.32 

Zinc 5.626 

A  Weston  0-150  voltmeter  combined  with  a  source  of  constant 
E.  M.  F. — e.  g.,  an  incandescent  street  circuit  of  about  100  volts, 
furnishes  a  convenient  and  quick  method  of  measuring  resistances 
of  from  5,000  to  100,000  ohms. 

Directions. — Form  a  circuit  of  the  voltmeter  and  x  in  series, 
connected  with  the  street  service.  Take  a  reading  of  the  volt- 
meter 9.  Suddenly  short-circuit  x  and  observe  the  new  deflection 
01.  Then,  if  E  be  the  resistance  of  the  voltmeter, 


x  = 


E  (Ol  -  0) 


Prove  the  correctness  of  the  formula.  Measure  resistances  of 
widely  varying  magnitude  (lead-pencil  marks  on  ground  glass) , 
and  plot  a  curve  with  x  as  abscissae  and  error  %  in  results  as  or- 
dinates. 


FIG.  403. 


Method  of  Wheatstone's  Bridge.— 

When  a  circuit  is  arranged  as  in  Fig.  403, 
there  will  be  no  current  in  the  galvanom- 
eter G,  if  the  resistances  a,  b,  E,  and  x 
are  so  proportioned  that  a  \  b  =  E  \  x. 

Apparatus. — Resistances  a  and  b,  rheo- 
stat E,  galvanometer,  source  of  E.  M.  F., 
commutator,  and  x. 


WIRE    BRIDGE.  459 

Directions  [a  =  b]. — Connect  apparatus  as  in  Fig.  404.     The 
commutator  c  serves  to  quickly  exchange  6  for  a  in  Fig.  403, 
and  hence,  if  a  be  not  exactly  equal  to  b, 
two  values  of  E  (E^  and  J22)  will  be  found  FiG^404. 

which  produce  an  equilibrium  in  the  bridge. 
The  true  value  of  x  will  then  be 


.=*fi 


x 


2 

Interpolation. — In  practice  it  is  seldom 
that  a  rheostat  has  sufficiently  small  units 
to  render  it  possible  to  effect  an  exact  ad- 
justment of  the  bridge.  The  value  of  x 
may  be  determined,  however,  by  interpola- 
tion. Suppose  that  a  resistance  E  in  the  rheostat  nearly  pro- 
duces equilibrium.  "When  the  commutator  is  in  its  two  positions 
1  and  2,  suppose  the  needle's  readings  to  be  m,  and  m2  divisions 
respectively.  Increase  E  by  a  small  amount  8,  and  observe  the  cor- 
responding readings  nl  and  ?i2.  Then 


x  =  E+         _      \      7*   _n]  & 

For  measuring  very  large  resistances,  b  should  be  made  larger 
than  a  (10,  100,  or  1,000  times).  E  must  then  be  multiplied  by 

the  ratio  -  to  get  x.     If  x  be  small,  a  is  made  larger  than  b.     In 
a 

these  cases  the  commutator  must  be  dispensed  with,  as  well  as 
the  increased  accuracy  which  it  affords. 

Wire  Bridge. — In  the  bridge  formula  x  =  -  E  it  is  imma- 
terial whether  the  absolute  values  of  b  and  a  be  known  or  not,  as 
long  as  the  ratio  -  be  known.  If  b  and  a  be  together  the  resist- 
ances offered  by  two  portions  of  a  stretched  uniform  wire,  and 
contact  be  made  between  a  and  b  with  the  galvanometer  by  means 

of  a  sliding  knife  edge,  the  ratio  -  will  be  equal  to  the  ratio  of 

the  two  lengths  of  the  wire  comprised  between  the  contact  and 
the  two  ends  of  the  wire  respectively.  For  the  resistances  offered 
by  two  wires  of  the  same  material  and  cross  section  are  propor- 
tional to  the  lengths  of  the  wires. 

Apparatus. — Stretched  wire  with  sliding  contact,  galvanometer, 
.standard  resistance  E}  source  of  E.  M.  F.,  and  x. 


460 


ELECTRICAL    MEASUREMENTS. 


Directions.  —  Connect  as  in  Fig.  405.  Slide  the  contact  c  along 
the  wire  a  b  until  the  galvanometer  shows 
no  deflection.  Measure  the  lengths  of  a 
and  b.  (The  whole  wire  is  usually  made 
1,000  units  long,  hence,  if  a  be  measured, 
6  =  1,000  -a.)  Then 


FIG.  405. 

,•— 

a 


By  comparing  Figs.  403  and  405  it  will  be  noticed  that  the  battery 
and  galvanometer  have  been  exchanged.     Why  ? 

Method  of  Mathiesen  and  Hockin. — To  compare  the  con- 
ductivities of  two  substances. 

Apparatus. — Two  wires  of  the  same  cross-section  made  of  the 
two  substances,  sensitive  galvanometer,  stretched  wire  with  slid- 
ing contact,  and  source  of  E.  M.  F. 

Directions. — Send  a  current  through   the  stretched  wire   in 
FIG  406  multiple  arc  with  the  two  wires 

1*1 1! \     wn^cu  are  *°  be  compared,  and 

ft       K          v   B  R  I     which   are   arranged    in    series 

with  each  other.  Connect  one 
terminal  of  the  galvanometer  to 
a  point  pt  of  one  of  the  wires. 
Connect  the  other  terminal  with 
a  point  q1  on  the  stretched  wire, 

so  that  no  current  flows  through  the  galvanometer.     Proceed  sim- 
ilarly with  pa0a,  psq5,  and  ptq4.     Then 

Resistances,^       Length  qtg^ 
Resistance  p3pt       Length  q3qt 


•-4.9X933&: 


Conductivity  A  _  Length 
Conductivity  B      Length 


Why? 


BATTERY  RESISTANCES. 

Method  of  Ohm. — Apparatus. — Galvanometer  of  low  resist- 
ance G,  rheostat,  cell  of  internal  resistance  x. 

Directions. — Form  a  circuit  of  cell,  rheostat,  and  galvanometer 
in  series.  Adjust  H  in  rheostat  so  as  to  give  a  proper  deflection  0. 
Add  a  resistance  Rf  in  the  rheostat  so  that  the  deflection  &  is- 


METHOD    OF    MANCE. 


461 


about,  half  0.     Then,  if  the  deflections  be  proportional  to  the  cur- 
rents, 

x  =  Rf  -~  ~  R  +  0- 


This  formula  results  from 

(1)  6  = 

(2) 


E 


G  +  x  + 
E 


~  G  +  R  +  R  +x 

A  Weston  ammeter  may  be  employed  in  place  of  the  galvanome- 
ter, and  it  yields  quick  results. 

Method  of  Mance. — Apparatus. — Galvanometer,  wire  bridge 
or  two  known  resistances,  rheostat,  key,  cell  of  internal  resistance  x. 

Directions. — Connect  the  cell  in  one 
arm  of  the  Wheatstone's  bridge,  and  in  FlG-  407. 

the  customary  position  of  the  battery 
place  a  key  and  suitable  resistance.  Ma- 
nipulate a,  6,  or  E  so  that  the  galva-< 
nometer  gives  the  same  deflection  whether 
the  key  be  closed  or  not.  Then 

*=•!* 

o 

The  magnitude  of  the  galvanometer  deflection  may  be  regulated 
by  a  copper  wire  shunted  between  its  terminals. 

This  method  is  unreliable  in  its  results.  The  E.  M.  F.  of  a 
cell  is  somewhat  dependent  on  the  current.  If  the  key  circuit  ia 
of  small  resistance,  the  E.  M.  F.  will  be  changed  by  the  closing  of 
the  key. 

Method  of  Thomson. — Apparatus. — Galvanometer,  rheostat, 


shunt  for  galvanometer,  cell  of  internal  resistance  x. 
Directions. — Connect  the  cell,  plugged  rheostat, 
and  shunted  galvanometer  in  series.  Adjust  shunt 
for  a  suitable  deflection.  Remove  shunt  of  resist- 
ance S  and  bring  in  circuit  a  resistance  -R  from 
rheostat,  so  as  to  produce  the  same  deflection  as 
before.  Jf  G  be  the  galvanometer  resistance,  then 

_ES 
x—  Q. 


FIG.  408. 


462  ELECTRICAL    MEASUREMENTS. 

The  current  C  in  the  galvanometer  is  the  same  in  each  observa- 
tion.    In  the  first  case 


In  the  second  case 

fi  — 

x  +  R  +  G 

whence 


„         0          G*S          GS 
Gx  +  Sx+  -=-—, 


G  +  S 

Method  of  Beetz. — Apparatus. — Stretched  wire  of  known 
resistance  per  unit  length  provided  with  two  sliding  contacts,  gal- 
vanometer, shunted  cell,  double  key,  cell  of  internal  resistance  x. 

Directions.  —  Connect  cir- 
cuit as  indicated  in  Fig.  409> 
both  cells  tending  to  send  a 
current  toward  A.  At  A  is  a 
key  connecting  both  cell  cir- 
cuits with  the  stretched  wire 
Ap.  Leaving  p  in  place,  shift 
o  until  no  deflection  occurs  in  the  galvanometer  G,  upon  suddenly 
closing  the  key  at  A.  Shift  p  to  a  new  position,  p',  and  find  a  cor- 
responding point,  o',  which  shall  produce  an  equilibrium.  Repre- 
senting the  resistances  of  Ao,  op,  Ao',  and  o'p'  by  a,  b,  a',  b',  re- 
spectively, we  have 

ab'  -  a'b 


x  = 


a'  -a 


minus  the  resistance  of  the  conducting  wires. 

Proof. — Inasmuch  as  no  current  flows  in  G,  the  current  C  In 
the  stretched  wire  is  the  same  as  in  the  branch  AEp.     Hence 

E  =  C  (x  +  a  +  b), 

if  we  neglect  connecting  wires.     Also  the  difference  of  potential 
V  between  A  and  o  is 

V=  Ca. 


RESISTIVITY    OF    ELECTROLYTES. 

In  the  second  adjustment  we  have 

E  =  G'  (x  +  a'  +  V) 

V=  C'a' 
E       x  +  a  +  b      x  +  a'  +  V 


463 


V 


aV  -  a'b 


This  method  gives  the  resistance  of  the  cell  E  on  open  circuit. 
It  may  also  be  used  to  determine  the  resistance  of  a  cell  which 
has  been  previously  short-circuited  through  a  resistance.  This 
resistance  can  be  thrown  out  at  the  moment  of  contact  at  A. 


FIG.  410. 


Method  of  Kohlrausch.  —  Apparatus.  —  Induction    coil  (of 
low  resistance  secondary),  cell  to  operate 
it,  telephone  receiver,  wire  bridge,  cell  of 
internal  resistance  x. 

Directions.  —  Connect  the  cell  in  one 
of  the  arms  of  the  Wheatstone's  bridge. 
Connect  the  secondary  of  the  induction 
coil  with  the  sliding  contact  and  the  junc- 
tion between  R  and  x.  Substitute  a  tele- 
phone for  the  galvanometer  of  an  ordinary 
bridge  combination.  Adjust  a  and  b  so 
that  a  minimum  loudness  is  heard  in  the 
telephone.  Then 


ft 


Why  can  a  telephone  be  used  and  not  a  galvanometer  ?     . 

Resistivity  of  Electrolytes  —  If  a  vessel  containing  an 
electrolyte  and  supplied  with  platinized  platinum  electrodes  be 
substituted  for  the  cell  in  Fig.  410,  the  resistance  of  the  electrolyte 
may  be  determined  in  the  same  manner  as  the  internal  resistance 
of  the  cell.  Owing  to  the  high  temperature  coefficient  of  electro- 
lytes the  vessel  should  be  placed  in  a  water  bath  in  order  to  main- 
tain the  temperature  constant.  The  temperature  of  the  electrolyte 
may  be  obtained  from  a  thermometer  with  its  bulb  submerged  in 
the  electrolyte,  if  the  vessel  is  of  suitable  shape.  If  the  contrary 
be  the  case,  the  temperatures  of  the  bath  and  electrolyte  may  be 
assumed  alike.  The  resistance  R  of  the  electrolyte  is  dependent 
on  the  size  and  shape  of  the  vessel  and  on  the  position  of  the  elec- 
trodes. To  obtain  the  resistivity  it  is  necessary  to  substitute  for 


464:  ELECTRICAL    MEASUREMENTS. 

the  electrolyte  another  of  known  resistivity  pf  and  obtain  its  re- 
sistance Rr.     Then  the  resistivity  of  the  original  electrolyte 


As  a  standard  solution  saturated  NaCl  (specific  gravity  =  1.201) 
may  be  used.  Its  resistivity  at  18°  is  4657  ohms.  This  decreases 
0.104  ohm  for  each  degree  rise  of  temperature. 

COMPARISON    OF   E.  M.  F.'S. 

The  Clark  standard  cell  has  an  E.  M.  F.  at  the  temperature  t  of 
1.434  [i  _  0.001l5(*  -  15)]  volts. 

It  should  never  be  short-circuited  or  closed  through  less  than 
10,000  ohms.  For  comparing  the  E.  M.  F.  #  of  a  cell  with  that  of 
the  standard  Es,  by  means  of  a  tangent  *  galvanometer,  we  have 
the  following  methods  : 

Method  of  Unequal  Resistances  and  Deflections  — 
Apparatus  __  Galvanometer,  resistance  -box,  standard  cell,  and 
cell  x. 

Directions.  —  Form  a  circuit  of  the  standard  cell  and  the  rhe- 
ostat with  resistance  Rs>  through  the  galvanometer  whose  reduction 
factor  is  K.  Observe  the  deflection  6S.  Substitute  x  for  the  stand- 
ard and  with  a  resistance  Rx  note  6X.  Then,  if  JBS  and  Bx  be  the 
resistances  of  the  standard  and  x  and  G  of  galvanometer,  we  have 


and 


. 

whence 

/q.  -  (Bx+Rx.x 

-(B.  +  R.+  0)to*.0.* 

Consider  whether  you  may  neglect  Bs  and  Bx. 

Method  of  Equal  Resistances.—  If  you  arrange  so  thai 
3X  +  Rx  +  a  =  B8  +  R8  +  G,  then  (3)  reduces  to 


*  Small  deflections  obtained  with  a  telescope  and  straight  scale  are  propor- 
tional to  the  tangents  of  the  angular  deflections  of  the  needle. 


POLARIZATION.  465 

Method  of  Equal  Deflections.— If  Ks  and  Rx  be  so  ad- 
justed that  6X  —  6S,  then 


Method  of  Sum  and  Difference.  —  Directions. — Connect 
both  standard  and  x  in  series  and  with  the  total  resistance  of  the 
circuit  R  of  such  a  [large]  magnitude  as  to  obtain  a  suitable  de- 
flection 0.  Reverse  one  of  the  cells  so  that  both  tend  to  send  cur- 
rents in  opposite  directions.  Note  the  deflection  &.  Then 

E9  +  x      tan.  6 


_ 
" 


—  x      tan.  0' 

tan.  0  -  tan.  & 
tan.  0  +  tan.  ff 


Method  of  Wheatstone  __  Directions.  —  Form  a  circuit  with 
standard  cell,  suitable  resistance,  and  galvanometer.  Note  deflec- 
tion 0.  Add  R8  to  the  circuit  and  note  deflection  &.  Substitute 
x  for  the  standard  and  adjust  resistance  so  as  to  obtain  0.  Add 
Rx  to  get  &.  Then 


Derive  the  formula. 

Polarization. — Apparatus. — Two  platinum  electrodes  in  a 
beaker  of  dilute  H2SO4,  Daniell  cell,  dead-beat  low  resistance 
•(shunted)  galvanometer,  key,  watch  with  seconds  hand,  and  rheo- 
stat. 

Directions. — Form  a  circuit  of  key,  cell,  1,000  ohms,  beaker, 
and  galvanometer  in  series.  Close  key  and  note  deflections  every 
thirty  seconds  for  ten  minutes.  Take  a  reading  at  the  instant  of 
closing,  if  possible.  Remove  the  platinums  and  heat  to  a  red  glow 
in  a  Bunsen  burner.  Replace  and  change  the  1,000  ohms  to  100 
ohms.  Repeat  the  operation  of  reading.  Reduce  the  resistance 
to  10  and  then  to  0  ohms.  Take  readings  every  fifteen  seconds 
in  the  last  two  cases.  Plot  the  four  resulting  curves  with  deflec- 
tions for  ordinates^and  time  for  abscissae.  What  inferences  can 
be  drawn  from  the  results  ?  What  causes  polarization  ?  How  is 
it  obviated  in  the  Daniell,  Bunsen,  and  Le  Clanche  cells  ?  Why 
lieat  the  platinum  ? 


466  ELECTRICAL    MEASUREMENTS. 


MEASUREMENT   OF   CURRENTS. 

Reduction   Factor  of  a  Galvanometer The  reduction 

factor  K  of  a  galvanometer  is  such  a  constant  that  the  current  G 
which  passes  through  the  galvanometer  is  expressed  as  a  function 
of  the  angular  deflection  <o  of  the  needle  by  the  equation 

G  =  K  tan.  CD. 

Apparatus. — Telescope-reading  galvanometer,  standard  Daniell 
cell,  rheostat,  and  meter  rod. 

Directions. — Measure  the  voltage  E  of  the  cell  and  the  re- 
sistance G  of  the  galvanometer.  Then  form  a  circuit  of  cell, 
galvanometer,  and  resistance-box.  Vary  the  resistances  E  in  the 
rheostat,  noting  the  corresponding  deflections  0.  Measure  the 
distance  d  of  the  middle  point  of  the  scale  from  the  galvanometer 
mirror.  [In  the  same  units  as  those  of  the  scale,  e.g.,  milli- 
metres.] Calculate  the  currents  from  E,  G,  and  E's.  Calcu- 
late the  <o's  from  the  formula 

A 

tan.  2  a)  —  - •• 
d 

Calculate  the  reduction  factors  K  for  the  different  currents  and 
make  a  table.  Plot  a  curve  with  tan.  o>  for  ordinates  and  G  for 
abscissae. 

The  currents  may  be  read  directly  by  inserting  a  Weston  am- 
meter, if  the  galvanometer  be  suited  for  moderately  strong  cur- 
rents. 


Reduction  Factor  of  an   Electro-dynamometer.—  If  a 

'current  (7,  flowing  through  an  electro-dynamometer,  needs  a  tor- 
sion angle  6  to  bring  the  needle  back  to  zero,  the  reduction  factor 
K  connects  G  and  6  by  the  formula 


Why? 

Apparatus.  —  Electro-dynamometer,  ammeter,  lamp-board  re- 
sistance, street  circuit. 

Directions.  —  Form  a  circuit  of  all  the  apparatus  in  series,  and 
varying  the  lamps  in  circuit,  note  C's  by  the  ammeter  and  corre- 
sponding e's  of  the  electro-dynamometer.  Calculate  K  in  each 
case  and  form  a  table.  Plot  a  curve  with  6's  for  ordinates  an& 
C's  for  abscissae. 


HEAT    EFFECTS. 


Electro-chemical  Equivalents  of  Copper  and  Hydro- 
gen. —  One  coulomb  [1  ampere  for  1  second]  theoretically  disen- 
gages 0.1157  cu.  cm.  of  hydrogen  [at  760  mm.  and  0°]  at  the 
cathode  of  an  electrolytic  vessel  containing  dilute  H2SO4,  and 
0.000328  gram  of  copper  from  a  solution  of  CuSO4. 

Apparatus.  —  Hoffman  H2SO4  voltameter  with  cock  at  the  bot- 
tom, copper  voltameter,  Weston  ammeter,  lamp-board,  street  cir- 
cuit, clock,  thermometer,  barometer. 

Directions.  —  Fill  the  voltameter  with  a  dilute  solution  of  chem- 
ically pure  H2SO4.  Form  a  fresh  deposit  on  the  cathode  of  the 
copper  voltameter.  Wash  the  cathode,  dry  it  under  an  air-pump, 
and  weigh.  Let  the  weight  be  'w  grams. 

Form  a  circuit  of  ammeter,  two  lamps  in  multiple  arc,  volta- 
meter in  series.  Close  the  circuit  and  note  the  time  t.  Allow  the 
current  to  flow  until  one  tube  of  the  voltameter  is  nearly  filled 
with  hydrogen.  Turn  off  current,  noting  time  t'.  Let  the  acid  run 
out  of  the  lower  cock  of  the  voltameter  until  the  level  in  the  reser- 
voir tube  is  the  same  as  in  the  hydrogen  tube.  Bead  off  the  cu. 
cms.  q  of  hydrogen.  Note  barometer  height  h.  Take  the  tem- 
perature t°  of  hydrogen  by  placing  the  thermometer  alongside  the 
tube.  Eead  the  ammeter  every  thirty  seconds  that  the  circuit 
is  closed.  Let  the  average  current  be  C.  Wash,  dry,  and  weigh 
[=  w'  grams]  the  copper  cathode.  C  (tf  —  t)  coulombs,  in  passing 
through  the  circuit,  have  deposited  (wf  —  w)  grams  of  copper  and 

cu-  cms-  °f  hydrogen. 


1  -f-  0.00367  t°   760 

Verify  the  theoretical  equivalents,  i.e.,  amount  per  coulomb  in 
each  case. 


Heat  Effects. — C  amperes  flowing  through  E  ohms  for  t  sec- 
onds liberate  C*Rtx  gram  calories  of  heat  You  are  required  to 
determine  x. 

Apparatus. — Calorimeter,  distilled  HaO,  thermometer,  bare 
German  silver  coil,  balance,  ammeter,  lamp-board  resistance,  and 
clock. 

Directions. — Measure  the  resistance  R  of  the  coil.  Submerge 
the  coil  in  q  grams  of  H2O  placed  in  the  calorimeter.  Place  the 
thermometer  so  that  the  bulb  is  in  the  centre  of  the  coil.  Con- 
nect the  lamp-board,  ammeter,  and  coil  in  series.  Close  the  cir- 
cuit and  note  the  time  tl  and  temperature  t°.  When  the  temper- 
ature [the  H2O  being  continually  stirred]  reaches  about  30°  [r=£2°], 
open  the  circuit,  noting  time  ttj.  Eead  the  ammeter  and  ther- 


468 


ELECTRICAL    MEASUREMENTS. 


mometer  every  thirty  seconds  that  the  circuit  is  closed.     If  the 
average  current  be  C  and  the  water  value  of  the  calorimeter  be  w, 

(1°  -  t°)  (w  +  q) 
G'B  (t,  -  0 

It  is  well  to  have  the  original  temperature  of  the  water  as 
much  below  the  temperature  of  the  room  as  it  will  be  above  that 
temperature  at  the  close  of  the  experiment.  Plot  a  curve  of  tem- 
perature and  time.  Explain  its  form. 


CONDENSERS. 

If  a  condenser  of  G  farads  capacity  be  charged  with  Q  coulombs, 
the  two  terminals  will  have  a  difference  of  potential  of  V  volts  de- 
termined by  the  condition  Q  =  C  V.  If  a  condenser  charged  suc- 
cessively with  Qlt  Q3 . . .  units  be  discharged  through  the  same  gal- 
vanometer yielding  the  [small]  amplitudes  of  the  first  vibrations 
6lt  0a  . .  .  then  Ql  :  Q3  :  . . .  =  6l  :  0a  :  . .  .  The  deflections  6  are 
termed  "throws"  or  "kicks0" 

To  Compare  Capacities. — Apparatus. — Double  key,  stand- 
ard condenser  (7,  condenser  of  capacity  x,  ballistic  galvanometer, 

and  Daniell  cell. 

Directions. — Connect  up  the  stand- 
ard as  in  Fig.  411.  Close  the  key  and 
observe  the  throw  0.  Substitute  the 
condenser  of  unknown  capacity  for  the 
standard.  Observe  the  throw  0'.  Then 


The  ratio  of  the  E.  M.  F.  of  two  cells  may  be  easily  determined 
by  means  of  the  condenser.  They  are  to  each  other  directly  as 
the  throws  which  they  cause  in  the  galvanometer  when  connected 
successively  with  the  same  condenser  as  in  Fig.  411. 

To  Determine  the  Internal  Re- 
sistance of  a  Cell  by  Means  of  a 
Condenser. — Apparatus. — Condenser, 
C,  ballistic  galvanometer,  G,  double 
contact  key,  K,  rheostat,  E,  and  cell  of 
internal  resistance  x. 

Directions. — Form  circuit  as  in  Fig. 
412,  leaving  out  an  infinity  plug  in  the 
rheostat.  Press  the  key  and  release  it. 
Observe  the  throw  6  in  the  galvanom- 


FIG.  412. 


MAGNETISM.  469 

•eter.  Replace  the  infinity  plug  leaving  a  resistance  R  in  the 
rheostat.  Again  close  and  release  the  key  observing  the  throw  &. 
Then 

,,     —'-¥• 

Prove  that  the  formula  is  correct. 


MAGNETISM. 

Moment  of  Inertia.  —  The  moment  of  inertia  K  of.  a  cylinder 
magnet  I  cms.  long  and  of  r  cms.  radius  and  weighing  m  grams, 
referred  to  an  axis  perpendicular  to  the  axis  of  the  cylinder  at  its 
middle  point  is 

'--(£+3- 

measure  I  by  a  scale,  2r  by  micrometer  screw,  and  m  by  a  balance. 
Calculate  K. 

Time  of  Oscillation  of  a  Cylindrical  Magnet.  —  Appara- 
tus. —  Cylinder  magnet,  suspension  case,  seconds  striking  clock. 

Directions.  —  Suspend  magnet  so  that,  when  no  torsion  is  ex- 
erted by  the  suspension,  the  magnet  sets  north  and  south.  Affix 
a  light  paper  pointer  to  magnet  over  a  mark  in  the  case.  Set  the 
magnet  in  vibration  by  approaching  another  magnet.  Starting 
at  any  convenient  time,  mentally  count  the  seconds  as  they  are 
struck  by  the  clock  and,  in  your  note-book,  record  the  exact  times 
of  50  successive  passages  of  the  pointer  over  the  mark  in  the  case. 
(Instead  of  a  pointer,  a  mirror  may  be  attached  to  the  magnet 
and  the  passage  of  the  zero  point  of  a  scale  can  be  observed  in  a 
telescope.)  The  seconds  must  be  divided  into  10  parts  by  esti- 
mate. A  little  practice  enables  one  to  do  this  well. 

Of  the  50  observed  times,  cast  away  the  first  5  and  the  last  5. 
Divide  the  remaining  40  into  4  groups  of  10  successive  times.  In 
each  group  take  the  arithmetical  mean  of  the  1st  and  10th,  2d 
and  9th,  3d  and  8th,  4th  and  7th,  5th  and  6th.  Take  the  mean  of 
the  means  of  each  group.  You  have  then  four  absolute  points  in 
time.  The  magnet  made  20  oscillations  between  the  1st  and 
3d  points  and  20  between  the  2d  and  4th  points.  The  time  of 

gd  _  p«         4*&  _  2<* 

a  single  oscillation  r  =  —  ^-  —  =  —  —  --     From  K  and  r  cal- 

M  =  magnetic  moment  of  the  cylinder, 
_  f.  ,   ,     .       ,  .  .  ,          * 

H  =  earth  s  horizontal  intensity. 


•culate  MH—  — 


Determination   of  —.—Apparatus.—  Magnetometer,  cylin- 
rl 


470  ELECTRICAL    MEASUREMENTS. 

der  magnet,  rack  to  hold  magnet  in  same  horizontal  plane  as  the> 
needle  of  the  magnetometer,  meter  rod. 

Directions.  —  Place  rack  so  as  to  hold  magnet  in  an  east-west 
direction  with  its  middle  point  in  the  same  horizontal  plane  as  the 
magnetometer  needle  and  directly  north  of  it.  Place  magnet  at  a 
distance  r  cms.  from  the  needle  and  read  the  deflection  6  of  the 
magnetometer  needle.  Reverse  the  magnet  end  for  end  and  read 
the  deflection  6'.  Average  these  readings.  Repeat  the  operation 
with  the  magnet  at  a  shorter  distance  r'  cms.  from  the  needle, 
obtaining  an  average  deflection  <£  (r  should  be  equal  to  about  1.4 
r').  Then 

M      r5  tan.  6  —  /6  tan.  <fr 


From  the  values  of  —   and  ME  determine  M  and  H.     Calculate 
Jd. 

M 

the  specific  magnetism  =  -    .  —  • 

wt.  in  grams 

Magnetization  Curve  of  Iron  or  Steel.  —  Apparatus.  — 
Test  ring*,  T,  wound  with  a  primary  and  secondary  coil,  ammeter, 
A,  adjustable  resistance,  R,  commutator,  C,  ballistic  galvanometer, 
G,  and  source  of  current,  E. 

Directions.  —  Connect  the  apparatus  as  in  Fig.  413.  Adjust  R 
so  as  to  yield  the  maximum  current  to  be  employed.  With  the 
galvanometer  circuit  broken,  cominutate  a  few  times  to  get  the 

iron  into  a  cyclic  condition. 
Close  the  galvanometer  circuit, 
and,  commutating  once,  ob- 
serve  the  throw  of  the  galva- 
nometer, 6,  at  the  same-  time 
read  the  amperes,  c,  by  the  am- 
meter. Repeat  this  operation  with  various  currents.  The  mag- 
netizing forces  are  proportional  to  the  current  strengths,  and  the 
induction  in  the  iron  is  proportional  to  the  throws  of  the  gal- 
vanometer. If  the  current  in  the  primary  of  N  turns  be  c  amperes 

*  The  dimensions  of  the  test  ring  and  the  number  of  turns  of  wire  in  the- 
primary  and  secondary  are  dependent  on  the  sensibility  of  the  galvanometer 
and  the  availability  of  current  for  the  primary  magnetizing  coil.  The  fol- 
lowing ring  is  suitable  for  a  test  with  the  cheap  D'Arsonval  galvanometers 
mentioned  before.  The  ring  is  annular,  of  rectangular  cross-section,  with 
an  internal  diameter  of  5  inches,  an  external  diameter  of  6  inches,  and  a 
depth  of  2  inches.  If  the  primary  be  wound  with  one  layer  of  No.  16  wire 
(250  turns),  5  amperes  will  be  the  maximum  current  required.  The  second- 
ary needs  but  4  or  5  turns. 


MAGNETIZATION    OF    IRON.  471 

and  the  arithmetical  mean  of  the  internal  and  external  diameters 
be  d  cms.,  the  magnetizing  force 


If  the  throw  6  in  the  galvanometer  connected  with  n  turns  around 
the  ring,  whose  cross-  section  is  A  square  cms.,  results  from  a  re-. 
versal  of  the  main  current,  c,  then  the  flux  density  corresponding 
to  this  Hia 

D      100  r  . 
B  —  £-—-  kQ  gausses, 
A  A.n 

where  r  is  the  resistance  of  the  galvanometer  plus  the  secondary 
coil,  and  k  is  the  galvanometer  coefficient,  i.e.,  the  micro-coulombs 
of  electricity  which  are  necessary  to  cause  a  throw  of  1  scale  di- 
vision in  the  galvanometer.  To  obtain  the  value  of  k  it  is  neces- 
sary to  charge  a  microfarad  condenser  with  a  cell  of  E  volts,  dis- 
charge it  through  the  galvanometer,  and  immediately  afterward 
connect  the  terminals  of  the  galvanometer  by  a  resistance  equal 
to  the  resistance  of  the  secondary  coil  on  the  ring.  This  latter  is 
necessary  because  the  damping  of  a  galvanometer  is  dependent 
on  the  external  resistance.  The  charge,  discharge,  and  short  cir- 
cuit can  be  conveniently  accomplished  with  the  assistance  of  a 
two-tongued  top-and-bottom  contact  key.  Plot  a  curve  with  B 
for  ordinates  and  H  for  abscissae. 

Test  Nail.  —  This  exercise  is  to  determine  the  distribution  of 
force  along  a  bar  magnet.  If  a  piece  of  soft  iron  be  placed  in  the 
field  of  a  magnet,  a  pole,  proportional  to  the  field's  strength,  will 
be  induced.  The  force  exerted  will  be  proportional  to  the  strength 
of  field  x  strength  of  pole,  i.e.,  proportional  to  the  square  of  the 
field  strength. 

Apparatus.  —  Bar  magnet,  piece  of  wood  of  the  same  size  as  the 
magnet,  soft  iron  armature,  suspended  from  a  spring  whose  elon- 
gation may  be  measured  on  a  graduated  circular  scale,  meter 
rod. 

Directions.  —  Determine  the  0  of  the  scale  with  the  armature 
resting  upon  the  piece  of  wood.  Substitute  for  the  wood  the 
magnet  and,  using  the  0  just  found,  determine  the  extension  of 
the  spring  necessary  to  detach  the  armature  from  various  points, 
of  the  magnet.  Kepresenting  the  distances  of  these  points  from 
the  middle  of  the  magnet  by  Z>,  and  the  extension  by  F,  form  a 


fW 

p  and  W  -=  • 


table  of  D,  F,       p  and  W  -=  •     Plot  a  curve  of  F  and  D. 


472  ELECTRICAL    MEASUREMENTS. 

CALIBRATIONS. 

Rheostat. — Apparatus.—  Wire  bridge,  galvanometer,  rheostat, 
1-ohm  coil,  and  standard  100-ohm  coil. 

Directions. — Determine  the  correction  for  the  500  division  of 
the  bridge  wire  by  balancing  two  10-ohm  coils  against  each  other 
and  then,  exchanging  them,  balancing  them  again.  The  mean  of 
the  two  bridge  readings  gives  the  electrical  centre  or  500  of  the 
wire.  (500  —  mean)  is  the  correction  which  must  be  applied  in  all 
the  subsequent  readings.  Now,  assuming  the  auxiliary  1  ohm  as 
correct,  determine  the  assumed  correct  value  of  the  1  ohm  in  the 
rheostat.  Compare  these  two  1  ohms  with  the  2-ohm  coil,  and 
find  its  assumed  correction.  Similarly  compare  3  with  corrected 
1  +  2  ;  4  with  3  +  1 ;  10  with  4  +  3  +  2  +  1;  20  with  10  +  4  + 
3  +  2  +  1 ;  etc.  You  thus  obtain  a  table  of  assumed  corrections, 
which  would  be  correct  at  the  correct  temperature  for  the  assumed 
standard  1-ohm  coil.  Now  compare  the  100  in  the  rheostat  with  the 
standard  100  coil.  From  the  actual  correction  for  the  100,  thus  ob- 
tained, subtract  the  assumed  correction.  Add  -£$  of  this  difference 
to  the  assumed  correction  for  the  10  ;  TJ7  to  the  assumed  correc- 
tion for  the  1 ;  T4ff  for  the  40  ;  etc.  Make  a  table  of  corrections. 

"Bridge  Wire. — From  the  known  values  of  the  resistances 
the  electrical  position  of  any  portion  of  the  bridge  wire  can  be 
obtained.  The  bridge  reading  minus  the  electrical  position  =  cor- 
rection. Find  the  correction  for  every  50th  division. 

Ammeter. — Apparatus. — Standard  ammeter,  adjustable  re- 
sistance, current  to  the  maximum  capacity  of  the  ammeter  to  be 
calibrated. 

Directions., — Arrange  all  the  apparatus  in  series.  Adjust  the  re- 
sistances so  as  to  produce  a  current  T^  of  the  maximum  range  of  the 
ammeter  to  be  calibrated.  Read  both  the  ammeters  at  the  same 
time.  Eepeat  this  operation  with  different  currents  throughout  the 
range  of  the  instrument.  Plot  a  curve  with  the  readings  of  the 
standard  for  abscissae  and  those  of  the  other  ammeter  for  ordinates. 

Voltmeter. — Apparatus. — Standard  voltmeter,  two  adjust- 
able resistances,  E.  M.  F.  to  the  maximum  capacity  of  the  voltme- 
ter to  be  calibrated. 

Directions. — Connect  the  two  resistsfhces  in  series  with  the 
E.  M.  F.  Connect  both  voltmeters  in  multiple  arc  with  the  ter- 
minals of  one  of  the  resistances.  By  manipulating  the  resistances 
impress  various  voltages  on  the  voltmeters,  making  simultaneous 
readings  from  the  two  instruments  at  each  of  the  voltages.  Plot 
3,  curve  as  in  the  case  of  the  ammeters. 


OF  THE 

UNIVERSITY 


UNIVEESTTY  OF  CALIFORNIA  LIBEAEY, 
BERKELEY 


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DEC  26  19?' 


lSw-4,'24 


